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%I #20 Feb 24 2023 09:14:00
%S 1,3,17,193,5427,463023,134675759,139917028089,527871326293913,
%T 7281357469833220843,368715613115281663650597,
%U 68787958348542935934247206953,47453320297069210448891035137347047
%N a(n) = Sum_{k=0..n} binomial(n,k) * binomial(2^k+n-1,n).
%H Seiichi Manyama, <a href="/A133991/b133991.txt">Table of n, a(n) for n = 0..59</a>
%F a(n) = (1/n!)*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)*(2^k+1)^n.
%F G.f.: Sum_{n>=0} (-log(1 - (2^n+1)*x))^n/n!.
%F a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Jun 08 2019
%t Table[Sum[(-1)^(n-k) * StirlingS1[n, k]*(2^k + 1)^n, {k, 0, n}]/n!, {n, 0, 12}] (* _Vaclav Kotesovec_, Jun 08 2019 *)
%o (PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(2^k+n-1, n)); \\ _Seiichi Manyama_, Feb 24 2023
%Y Cf. A133990, A134173, A134174.
%K easy,nonn
%O 0,2
%A _Paul D. Hanna_ and _Vladeta Jovovic_, Jan 21 2008
%E More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
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