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

Offset: 1

Author

Paul D. Hanna, Feb 03 2011

Keywords

• tabl
• nonn

Examples

			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; ...
		

Crossrefs

Cf. columns: A000169, A185756, A185757; row sums: A185523.

Cf. diagonals: A112317, A185758, A185759.

Programs

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)}

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.