A218141 a(n) = Stirling2(n^2, n).

1, 1, 7, 3025, 171798901, 2436684974110751, 14204422416132896951197888, 50789872166903636182659702516635946082, 155440114706926165785630654089245708839702615196926765, 541500903058656141876322139677626107784896646583041951351456223689104719

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..25

Formula

a(n) = [x^n] Sum_{k>=0} k^(n*k) * exp(-k^n*x) * x^k / k!.

a(n) = [x^(n^2-n)] 1 / Product_{k=1..n} (1-k*x).

a(n) ~ n^(n^2)/n!. - Vaclav Kotesovec, May 11 2014

Example

O.g.f.: A(x) = 1 + x + 7*x^2 + 3025*x^3 + 171798901*x^4 + 2436684974110751*x^5 +...

Mathematica

Table[StirlingS2[n^2, n], {n, 0, 10}] (* Vaclav Kotesovec, May 11 2014 *)

Prog

(PARI) {a(n)=polcoeff(sum(k=0, n, (k^n)^k*exp(-k^n*x +x*O(x^n))*x^k/k!), n)}
(PARI) {a(n)=polcoeff(1/prod(k=1, n, 1-k*x +x*O(x^(n^2+1))), n^2-n)}
(PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n) = Stirling2(n^2, n)}
for(n=0, 10, print1(a(n), ", "))
(Maxima) makelist(stirling2(n^2, n), n, 0, 30 ); /* Martin Ettl, Oct 21 2012 */

Crossrefs

Cf. A008277, A218142, A218143, A007820, A217913, A217914, A217915.

Sequence in context: A242851 A264787 A070227 * A172956 A236368 A350018

Adjacent sequences: A218138 A218139 A218140 * A218142 A218143 A218144

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2012

Status

approved