OFFSET
0,2
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!.
EXAMPLE
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! +...).
PROG
(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), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 07 2012
STATUS
approved