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<n, as read by rows.

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

1,2

Links

Table of n, a(n) for n=1..36.

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: A143146 A298663 A325936 * A278458 A309705 A290604

Adjacent sequences: A185752 A185753 A185754 * A185756 A185757 A185758

Keyword

tabl,nonn

Author

Paul D. Hanna, Feb 03 2011

Status

approved