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%I #16 Apr 10 2022 01:55:49
%S 1,0,1,3,10,36,145,666,3466,19956,124111,821601,5755987,42634089,
%T 333827776,2759262897,24000288202,218806121205,2082848200057,
%U 20639203885008,212441617055458,2268057343273491,25085332185250564,287096974919978292,3395697093278589844
%N Expansion of Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - 3 * j * x).
%H Seiichi Manyama, <a href="/A353262/b353262.txt">Table of n, a(n) for n = 0..549</a>
%F a(n) = Sum_{k=0..floor(n/2)} 3^(n-2*k) * Stirling2(n-k,k).
%t a[n_] := Sum[3^(n-2*k) * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* _Amiram Eldar_, Apr 09 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k)/prod(j=1, k, 1-3*j*x)))
%o (PARI) a(n) = sum(k=0, n\2, 3^(n-2*k)*stirling(n-k, k, 2));
%Y Cf. A119429, A171367.
%Y Cf. A353256.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Apr 09 2022
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