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%I #24 Dec 22 2022 04:15:39
%S 1,11,231,7161,293601,14973651,913392711,64850882481,5252921480961,
%T 478015854767451,48279601331512551,5359035747797893161,
%U 648443325483545072481,84946075638344404495011,11977396665006561033796551,1808586896415990716103279201,291182490322974505292627951361
%N 10-factorial numbers.
%H G. C. Greubel, <a href="/A045757/b045757.txt">Table of n, a(n) for n = 1..323</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F a(n) = Pochhammer(1/10,n)*10^n.
%F a(n+1) = (10*n+1)(!^10) = Product_{k=0..n} (10*k+1), n >= 0.
%F E.g.f.: -1 + (1-10*x)^(-1/10).
%F Sum_{n>=1} 1/a(n) = (e/10^9)^(1/10)*(Gamma(1/10) - Gamma(1/10, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p G(x):=-1+(1-10*x)^(-1/10): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=1..14); # _Zerinvary Lajos_, Apr 03 2009
%p seq(mul(10*j+1, j = 0..n-1), n = 1..20); # _G. C. Greubel_, Nov 11 2019
%t FoldList[Times,10*Range[0,20]+1] (* _Harvey P. Dale_, Dec 02 2016 *)
%o (PARI) vector(21, n, prod(j=0,n-1, 10*j+1) ) \\ _G. C. Greubel_, Nov 11 2019
%o (Magma) [(&*[10*j+1: j in [0..n-1]]): n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o (Sage) [product( (10*j+1) for j in (0..n-1)) for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([1..20], n-> Product([0..n-1], j-> 10*j+1) ); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A035265, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.
%Y Cf. A008542, A048176.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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