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

0,2

Comments

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

Links

Table of n, a(n) for n=0..39.

Example

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; ...

Prog

(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)}

Crossrefs

Cf. A108267, A060543, A108290, A000169.

Sequence in context: A108290 A308804 A364709 * A019615 A132744 A059604

Adjacent sequences: A108288 A108289 A108290 * A108292 A108293 A108294

Keyword

nonn,tabl

Author

Paul D. Hanna, May 31 2005

Status

approved