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%I #5 Nov 26 2016 18:05:31
%S 1,2,9,61,550,6195,83837,1326923,24078588,493309850,11271757335,
%T 284379843234,7856320956198,235986714918110,7660827258318780,
%U 267365373971139600,9985779421324740445,397508459931685273305
%N Column 3 of triangle A107880.
%F G.f.: 1 = Sum_{k>=0} a(k)*x^k*(1-x)^((k+2)*(k+3)/2 - 1).
%e 1 = 1*(1-x)^2 + 2*x*(1-x)^5 + 9*x^2*(1-x)^9 +
%e 61*x^3*(1-x)^14 + 550*x^4*(1-x)^20 + 6195*x^5*(1-x)^27 +...
%t a[ n_, k_: 0, j_: 2] := If[n < 1, Boole[n >= 0], a[ n, k, j] = Sum[ a[ n - 1, i, j + 1], {i, k + j}]]; (* _Michael Somos_, Nov 26 2016 *)
%o (PARI) {a(n)=polcoeff(1-sum(k=0,n-1,a(k)*x^k*(1-x+x*O(x^n))^((k+2)*(k+3)/2-1)),n)}
%Y Cf. A107880, A107881, A107882.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 04 2005
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