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 A185755 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
 1, 2, 2, 9, 15, 6, 64, 154, 120, 30, 625, 1995, 2340, 1190, 220, 7776, 31191, 49315, 38325, 14595, 2170, 117649, 571221, 1142932, 1204588, 704102, 215950, 27076, 2097152, 11992688, 29141994, 38972388, 30945432, 14570976, 3761310, 409836 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA T(n,0) = A000169(n) = n^(n-1). T(n,n) = A112317(n). Sum_{k=0..n-1} T(n,k) = A185523(n). Sum_{k=0..n-1} (-1)^k*T(n,k) = 0^n. EXAMPLE Triangle begins: 1; 2, 2; 9, 15, 6; 64, 154, 120, 30; 625, 1995, 2340, 1190, 220; 7776, 31191, 49315, 38325, 14595, 2170; 117649, 571221, 1142932, 1204588, 704102, 215950, 27076; 2097152, 11992688, 29141994, 38972388, 30945432, 14570976, 3761310, 409836; 43046721, 283976517, 814059798, 1323693384, 1334427720, 853356072, 337738758, 75550188, 7303164; ... PROG (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)} CROSSREFS Cf. columns: A000169, A185756, A185757; row sums: A185523. Cf. diagonals: A112317, A185758, A185759. Sequence in context: A248665 A066324 A143146 * A278458 A039796 A224244 Adjacent sequences:  A185752 A185753 A185754 * A185756 A185757 A185758 KEYWORD tabl,nonn AUTHOR Paul D. Hanna, Feb 03 2011 STATUS approved

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