A211250 E.g.f.: exp(-1)*Sum_{n>=0} (1+x)^(n^3)/n!.

1, 5, 198, 20548, 4088918, 1341552690, 661685880676, 460785157967228, 432879460822014552, 529918744425680488240, 822575286838815581568992, 1583737023708711008926884072, 3713773722396456674797120593784, 10445266376618187161982580673417192

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = Sum_{k=0..n} Stirling1(n, k)*Bell(3*k).

a(n) = n!*exp(-1)*Sum_{k>=[n^(1/3)]} binomial(k^3,n)/k!.

Example

E.g.f.: A(x) = 1 + 5*x + 198*x^2/2! + 20548*x^3/3! + 4088918*x^4/4! +...
such that
A(x) = exp(-1)*(1 + (1+x) + (1+x)^8/2! + (1+x)^27/3! + (1+x)^64/4! +...).

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

Crossrefs

Cf. A000110 (Bell), A014507, A211251, A211252.

Sequence in context: A114351 A296172 A080927 * A208462 A107445 A106990

Adjacent sequences: A211247 A211248 A211249 * A211251 A211252 A211253

Keyword

nonn

Author

Paul D. Hanna, Apr 07 2012

Status

approved