A211252 E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^5)/n!.

1, 52, 115923, 1382610724, 51715861759515, 4638073139045397206, 846679440053068198564757, 281582422101970811697025996458, 157442703858164474987714673019721909, 139252837198831456324098952617013102583100, 185718002275320639405130518085966960592675564591

Offset: 0

Author

Paul D. Hanna, Apr 07 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 52*x + 115923*x^2/2! + 1382610724*x^3/3! + 51715861759515*x^4/4! +...
such that
A(x) = exp(-1)*(1 + (1+x) + (1+x)^32/2! + (1+x)^243/3! + (1+x)^1024/4! +...).
		

Crossrefs

Cf. A000110 (Bell), A014507, A211250, A211251.

Programs

PARI

{Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}
{Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)}
{a(n)=sum(k=0, n, Stirling1(n, k)*Bell(5*k))}
for(n=0,15,print1(a(n),", "))

Formula

a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(5*k).

a(n) = n!*exp(-1)*Sum_{k>=[n^(1/5)]} binomial(k^5,n)/k!.