cp's OEIS Frontend

A126463 Column 3 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}.

%I A126463 #3 Mar 30 2012 18:37:02
%S A126463 1,1,10,195,5940,257300,14989472,1130000385,107089958760,
%T A126463 12470885416545,1751753684302150,292264756622072214,
%U A126463 57165584968923450000,12962148519535236156640,3374220800446022166695530
%N A126463 Column 3 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 9*k + 20)*k/6, k>=0}.
%F A126463 G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 12*k + 41)*k/6].
%e A126463 Equals the number of subpartitions of the partition:
%e A126463 {(k^2 + 12*k + 41)*k/6, k>=0} = [0,9,23,43,70,105,149,203,268,345,...]
%e A126463 as illustrated by g.f.:
%e A126463 1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^9 + 10*x^2*(1-x)^23 + 195*x^3*(1-x)^43 + 5940*x^4*(1-x)^70 + 257300*x^5*(1-x)^105 + 14989472*x^6*(1-x)^149 + 1130000385*x^7*(1-x)^203 ...
%o A126463 (PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(1+(k^2+12*k+41)*k/6)),n)}
%Y A126463 Cf. A126460; A126461, A126462, A126464.
%K A126463 nonn
%O A126463 0,3
%A A126463 _Paul D. Hanna_, Dec 27 2006