A183604 E.g.f.: Sum_{n>=0} (1+x)^(n^2)*x^n/n!.

1, 1, 3, 13, 109, 1041, 14191, 236293, 4712793, 113061889, 3149562331, 100617526461, 3660463878853, 149772851618833, 6831434952176199, 345197855050549621, 19198332224485686961, 1168264651674879727233

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 109*x^4/4! +...
A(x) = 1 + (1+x)*x + (1+x)^4*x^2/2! + (1+x)^9*x^3/3! + (1+x)^16*x^4/4! +...

Mathematica

With[{nn=20}, CoefficientList[Series[Sum[(1+x)^n^2 x^n/n!, {n, 0, nn}], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 28 2021 *)

Prog

(PARI) {a(n)=n!*polcoeff(sum(m=0, n, x^m*(1+x+x*O(x^n))^(m^2)/m!), n)}

Crossrefs

Sequence in context: A333736 A220704 A061377 * A228563 A222863 A223911

Adjacent sequences: A183601 A183602 A183603 * A183605 A183606 A183607

Keyword

nonn

Author

Paul D. Hanna, Jan 12 2011

Status

approved