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%I #8 Mar 30 2012 18:37:26
%S 1,2,2,9,15,6,64,154,120,30,625,1995,2340,1190,220,7776,31191,49315,
%T 38325,14595,2170,117649,571221,1142932,1204588,704102,215950,27076,
%U 2097152,11992688,29141994,38972388,30945432,14570976,3761310,409836
%N Triangle: T(n,k) equals the coefficient of x^n*y^k in the n-th iteration of x*(1+xy)/(1-x), for n>=1, 0<=k<n, as read by rows.
%F T(n,0) = A000169(n) = n^(n-1).
%F T(n,n) = A112317(n).
%F Sum_{k=0..n-1} T(n,k) = A185523(n).
%F Sum_{k=0..n-1} (-1)^k*T(n,k) = 0^n.
%e Triangle begins:
%e 1;
%e 2, 2;
%e 9, 15, 6;
%e 64, 154, 120, 30;
%e 625, 1995, 2340, 1190, 220;
%e 7776, 31191, 49315, 38325, 14595, 2170;
%e 117649, 571221, 1142932, 1204588, 704102, 215950, 27076;
%e 2097152, 11992688, 29141994, 38972388, 30945432, 14570976, 3761310, 409836;
%e 43046721, 283976517, 814059798, 1323693384, 1334427720, 853356072, 337738758, 75550188, 7303164; ...
%o (PARI) {T(n,k)=local(A=x, G=x*(1+x*y)/(1-x)); for(i=1, n, A=subst(G, x, A+x*O(x^n)));polcoeff(polcoeff(A, n,x),k,y)}
%Y Cf. columns: A000169, A185756, A185757; row sums: A185523.
%Y Cf. diagonals: A112317, A185758, A185759.
%K tabl,nonn
%O 1,2
%A _Paul D. Hanna_, Feb 03 2011
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