%I #2 Mar 31 2012 20:25:45
%S 1,2,12,224,10480,953192,142380112,31483710848,9628770928896,
%T 3883258826234432,1993590236304413824,1267882998458215791104,
%U 977550890979543106650112,897784324116559558728995584
%N a(n) = A132878(n)/[(n+1)*(n+2)/2] for n>=0, where A132878 is column 1 of triangle A132870.
%C Triangle T=A132875 obeys: the g.f. of row n of T^n = (y + n*(n+1))^n for n>=0.
%o (PARI) {a(n)=local(M=Mat([1,0;1,1]),N,L);for(i=1,n,N=M; M=matrix(#N+1,#N+1,r,c,if(r>=c,if(r<=#N,(N^(#N))[r,c], polcoeff((x+(#M)*(#M+1))^(#M),c-1)))); L=sum(i=1,#M,-(M^0-M)^i/i);M=sum(i=0,#M,(L/#N)^i/i!);); M[n+2,2]*2/(n+1)/(n+2)}
%Y Cf. A132875, A132876, A132877, A132878.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Sep 29 2007