OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..30
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
EXAMPLE
O.g.f.: A(x) = 1 + x + 3*x^2 + 90*x^3 + 34105*x^4 + 210766920*x^5 + 26585679462804*x^6 +...
MATHEMATICA
Table[StirlingS2[n*(n+1)/2, n], {n, 0, 10}] (* Vaclav Kotesovec, May 11 2014 *)
PROG
(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), ", "))
(Maxima) makelist(stirling2(n*(n+1)/2, n), n, 0, 30 ); /* Martin Ettl, Oct 21 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 21 2012
STATUS
approved