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%I #3 Mar 30 2012 18:37:02
%S 1,1,1,3,21,274,5806,182766,8034916,471517614,35682799508,
%T 3388864405941,395127873991296,55543575452873070,9271180003481197642,
%U 1813921568747948684475,411378931233397975750296
%N Column 0 of triangle A126460; equals the number of subpartitions of the partition {(k^2 + 3*k - 4)*k/6, k>=0}.
%C When shifted left, equals column 1 of triangle A126460, which is the number of subpartitions of partition: {(k^2 + 6*k + 5)*k/6, k>=0}.
%F G.f.: 1/(1-x) = Sum_{k>=0} a(k)*x^k*(1-x)^[(k^2 + 3*k - 4)*k/6].
%e Equals the number of subpartitions of the partition:
%e {(k^2 + 3*k - 4)*k/6, k>=0} = [0,0,2,7,16,30,50,77,112,156,210,275,...]
%e as illustrated by g.f.:
%e 1/(1-x) = 1*(1-x)^0 + 1*x*(1-x)^0 + 1*x^2*(1-x)^2 + 3*x^3*(1-x)^7 + 21*x^4*(1-x)^16 + 274*x^5*(1-x)^30 + 5806*x^6*(1-x)^50 + 182766*x^7*(1-x)^77 ...
%o (PARI) {a(n)=polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x+x*O(x^n))^(1+(k^2+3*k-4)*k/6)), n)}
%Y Cf. A126460; A126462, A126463, A126464.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Dec 27 2006
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