A108291 Triangle, read by rows, resulting from the matrix product of triangle A108267 with Pascal's triangle (A007318).

1, 2, 1, 9, 9, 1, 64, 96, 34, 1, 625, 1250, 750, 125, 1, 7776, 19440, 16470, 5265, 461, 1, 117649, 352947, 386561, 184877, 35329, 1715, 1, 2097152, 7340032, 9863168, 6307840, 1913408, 232288, 6434, 1, 43046721, 172186884, 274223556, 220016574

Offset: 0

Author

Paul D. Hanna, May 31 2005

Keywords

• nonn
• tabl

Comments

Row sums form A108292. Column 0 is A000169(n) = (n+1)^n. Triangle with rows reversed is A108290.

Examples

			Triangle begins:
1;
2,1;
9,9,1;
64,96,34,1;
625,1250,750,125,1;
7776,19440,16470,5265,461,1;
117649,352947,386561,184877,35329,1715,1;
2097152,7340032,9863168,6307840,1913408,232288,6434,1; ...
		

Crossrefs

Cf. A108267, A060543, A108290, A000169.

Programs

PARI

{T(n,k)=local(X=x+x*O(x^(n-k))); polcoeff(sum(j=0,n,binomial(n+n*j+j,n*j+j)*(x/(1+X))^j)/(1+X),n-k)}