A211251 E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^4)/n!.

1, 15, 4125, 4201207, 10454906015, 51619504083157, 445183896786430439, 6151183312376366042809, 127892318444027363237894001, 3815107763405827557700743314007, 157278812586433713743644391748289829, 8693308684725580082237757157480179540583

Offset: 0

Author

Paul D. Hanna, Apr 07 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 15*x + 4125*x^2/2! + 4201207*x^3/3! + 10454906015*x^4/4! +...
such that
A(x) = exp(-1)*(1 + (1+x) + (1+x)^16/2! + (1+x)^81/3! + (1+x)^256/4! +...).
		

Crossrefs

Cf. A000110 (Bell), A014507, A211250, A211252.

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(4*k))}
for(n=0,15,print1(a(n),", "))

Formula

a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(4*k).

a(n) = n!*exp(-1)*Sum_{k>=[n^(1/4)]} binomial(k^4,n)/k!.