A218143 - OEIS

%I #14 May 11 2014 16:42:35

%S 1,1,3,90,34105,210766920,26585679462804,82892803728383735268,

%T 7529580759157036060608585183,22982258052528294182955639980819773510,

%U 2672446997421818663856559987803834697952486978300,13239043631590111512460321918828937597837325561187113535696980

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

%H Paul D. Hanna, <a href="/A218143/b218143.txt">Table of n, a(n) for n = 0..30</a>

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

%F a(n) ~ n^(n*(n+1)/2)/n!. - _Vaclav Kotesovec_, May 11 2014

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

%t Table[StirlingS2[n*(n+1)/2, n],{n,0,10}] (* _Vaclav Kotesovec_, May 11 2014 *)

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

%o (PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}

%o {a(n) = Stirling2(n*(n+1)/2, n)}

%o for(n=0, 15, print1(a(n), ", "))

%o (Maxima) makelist(stirling2(n*(n+1)/2,n),n,0,30 ); /* _Martin Ettl_, Oct 21 2012 */

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 21 2012