A108291 - OEIS

%I #3 Mar 30 2012 18:36:46

%S 1,2,1,9,9,1,64,96,34,1,625,1250,750,125,1,7776,19440,16470,5265,461,

%T 1,117649,352947,386561,184877,35329,1715,1,2097152,7340032,9863168,

%U 6307840,1913408,232288,6434,1,43046721,172186884,274223556,220016574

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

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

%e Triangle begins:

%e 1;

%e 2,1;

%e 9,9,1;

%e 64,96,34,1;

%e 625,1250,750,125,1;

%e 7776,19440,16470,5265,461,1;

%e 117649,352947,386561,184877,35329,1715,1;

%e 2097152,7340032,9863168,6307840,1913408,232288,6434,1; ...

%o (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)}

%Y Cf. A108267, A060543, A108290, A000169.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, May 31 2005