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%I #48 May 10 2024 11:09:10
%S 2,5,13,35,103,345,1325,5911,30067,172237,1096319,7677155,58648421,
%T 485377457,4326008691,41310343279,420783672791,4553946567241,
%U 52184383350787,631210595896453,8036822912123765,107444407853010597,1504827158220643895,22034062627659931905
%N Boustrophedon transform of primes.
%H Reinhard Zumkeller, <a href="/A000747/b000747.txt">Table of n, a(n) for n = 0..400</a>
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SeidelTransform">An old operation on sequences: the Seidel transform</a>.
%H J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54 (<a href="http://neilsloane.com/doc/bous.txt">Abstract</a>, <a href="http://neilsloane.com/doc/bous.pdf">pdf</a>, <a href="http://neilsloane.com/doc/bous.ps">ps</a>).
%H J. Millar, N. J. A. Sloane, and N. E. Young, <a href="https://doi.org/10.1006/jcta.1996.0087">A new operation on sequences: the Boustrophedon transform</a>, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.
%H Ludwig Seidel, <a href="https://babel.hathitrust.org/cgi/pt?id=hvd.32044092897461&view=1up&seq=175">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the <a href="https://www.hathitrust.org/accessibility">HATHI TRUST Digital Library</a>]
%H Ludwig Seidel, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1877_0157-0187.pdf">Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen</a>, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through <a href="https://de.wikipedia.org/wiki/ZOBODAT">ZOBODAT</a>]
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>.
%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F a(n) = Sum_{k=0..n} A109449(n,k)*A000040(k+1). - _Reinhard Zumkeller_, Nov 03 2013
%F E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+1)*x^k/k!. - _Ilya Gutkovskiy_, Jun 26 2018
%t t[n_, 0] := Prime[n+1]; t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, 30, 0] (* _Jean-François Alcover_, Feb 12 2016 *)
%o (Haskell)
%o a000747 n = sum $ zipWith (*) (a109449_row n) a000040_list
%o -- _Reinhard Zumkeller_, Nov 03 2013
%o (Python)
%o from itertools import islice, count, accumulate
%o from sympy import prime
%o def A000747_gen(): # generator of terms
%o blist = tuple()
%o for i in count(1):
%o yield (blist := tuple(accumulate(reversed(blist),initial=prime(i))))[-1]
%o A000747_list = list(islice(A000747_gen(),30)) # _Chai Wah Wu_, Jun 11 2022
%Y Cf. A000040, A109449, A230953, A230956, A230954, A230955.
%K nonn,changed
%O 0,1
%A _N. J. A. Sloane_
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