A218143 a(n) = Stirling2(n*(n+1)/2, n).

1, 1, 3, 90, 34105, 210766920, 26585679462804, 82892803728383735268, 7529580759157036060608585183, 22982258052528294182955639980819773510, 2672446997421818663856559987803834697952486978300, 13239043631590111512460321918828937597837325561187113535696980

Offset: 0

Author

Paul D. Hanna, Oct 21 2012

Keywords

• nonn

Examples

			O.g.f.: A(x) = 1 + x + 3*x^2 + 90*x^3 + 34105*x^4 + 210766920*x^5 + 26585679462804*x^6 +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A008277, A218141, A218142, A007820, A217913, A217914, A217915.

Programs

Mathematica

Table[StirlingS2[n*(n+1)/2, n],{n,0,10}] (* Vaclav Kotesovec, May 11 2014 *)

Maxima

makelist(stirling2(n*(n+1)/2,n),n,0,30 ); /* Martin Ettl, Oct 21 2012 */

PARI

{a(n)=polcoeff(1/prod(k=1, n, 1-k*x +x*O(x^(n*(n-1)/2))), n*(n-1)/2)}

PARI

{Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n) = Stirling2(n*(n+1)/2, n)}
for(n=0, 15, print1(a(n), ", "))

Formula

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

a(n) ~ n^(n*(n+1)/2)/n!. - Vaclav Kotesovec, May 11 2014