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A133991 a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2^k+n-1,n). 1
1, 3, 17, 193, 5427, 463023, 134675759, 139917028089, 527871326293913, 7281357469833220843, 368715613115281663650597, 68787958348542935934247206953, 47453320297069210448891035137347047 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

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 *)

CROSSREFS

Sequence in context: A195067 A158885 A202424 * A210898 A009494 A267659

Adjacent sequences:  A133988 A133989 A133990 * A133992 A133993 A133994

KEYWORD

easy,nonn

AUTHOR

_Paul Hanna_ and Vladeta Jovovic, Jan 21 2008

EXTENSIONS

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008

STATUS

approved

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Last modified September 18 02:20 EDT 2019. Contains 327149 sequences. (Running on oeis4.)