A211252 - OEIS

%I #5 Apr 07 2012 17:13:28

%S 1,52,115923,1382610724,51715861759515,4638073139045397206,

%T 846679440053068198564757,281582422101970811697025996458,

%U 157442703858164474987714673019721909,139252837198831456324098952617013102583100,185718002275320639405130518085966960592675564591

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

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

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

%e E.g.f.: A(x) = 1 + 52*x + 115923*x^2/2! + 1382610724*x^3/3! + 51715861759515*x^4/4! +...

%e such that

%e A(x) = exp(-1)*(1 + (1+x) + (1+x)^32/2! + (1+x)^243/3! + (1+x)^1024/4! +...).

%o (PARI) {Stirling1(n, k)=n!*polcoeff(binomial(x, n), k)}

%o {Bell(n)=n!*polcoeff(exp(exp(x+x*O(x^n))-1), n)}

%o {a(n)=sum(k=0, n, Stirling1(n, k)*Bell(5*k))}

%o for(n=0,15,print1(a(n),", "))

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Apr 07 2012