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A133991
a(n) = Sum_{k=0..n} binomial(n,k) * binomial(2^k+n-1,n).
2
1, 3, 17, 193, 5427, 463023, 134675759, 139917028089, 527871326293913, 7281357469833220843, 368715613115281663650597, 68787958348542935934247206953, 47453320297069210448891035137347047
OFFSET
0,2
LINKS
FORMULA
a(n) = (1/n!)*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)*(2^k+1)^n.
G.f.: Sum_{n>=0} (-log(1 - (2^n+1)*x))^n/n!.
a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jun 08 2019
MATHEMATICA
Table[Sum[(-1)^(n-k) * StirlingS1[n, k]*(2^k + 1)^n, {k, 0, n}]/n!, {n, 0, 12}] (* Vaclav Kotesovec, Jun 08 2019 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(2^k+n-1, n)); \\ Seiichi Manyama, Feb 24 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
STATUS
approved