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

%I A108291 #3 Mar 30 2012 18:36:46
%S A108291 1,2,1,9,9,1,64,96,34,1,625,1250,750,125,1,7776,19440,16470,5265,461,
%T A108291 1,117649,352947,386561,184877,35329,1715,1,2097152,7340032,9863168,
%U A108291 6307840,1913408,232288,6434,1,43046721,172186884,274223556,220016574
%N A108291 Triangle, read by rows, resulting from the matrix product of triangle A108267 with Pascal's triangle (A007318).
%C A108291 Row sums form A108292. Column 0 is A000169(n) = (n+1)^n. Triangle with rows reversed is A108290.
%e A108291 Triangle begins:
%e A108291 1;
%e A108291 2,1;
%e A108291 9,9,1;
%e A108291 64,96,34,1;
%e A108291 625,1250,750,125,1;
%e A108291 7776,19440,16470,5265,461,1;
%e A108291 117649,352947,386561,184877,35329,1715,1;
%e A108291 2097152,7340032,9863168,6307840,1913408,232288,6434,1; ...
%o A108291 (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 A108291 Cf. A108267, A060543, A108290, A000169.
%K A108291 nonn,tabl
%O A108291 0,2
%A A108291 _Paul D. Hanna_, May 31 2005