A263004 Row sums of the partition array for the products of the hook lengths numbers of Ferrers (or Young) diagrams A263003.

1, 1, 4, 15, 76, 368, 2365, 14892, 116236, 966064, 9256889, 96638496, 1129309316, 14261533248, 196315312964, 2900635720869, 45926240752560, 773725147192412, 13831256551416480, 261227089570409028, 5198858467673903360, 108706624576630569271

Offset: 0

Author

Wolfdieter Lang, Oct 08 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..60

Crossrefs

Cf. A066183, A117506, A263003.

Programs

Maple

h:= l-> (n-> mul(mul(1+l[i]-j+add(`if`(l[k]>=j, 1, 0),
             k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):
g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), `if`(i<1, 0,
                `if`(i>n, 0, g(n-i, i, [l[], i]))+g(n, i-1, l))):
a:= n-> g(n$2, []):
seq(a(n), n=0..22);  # Alois P. Heinz, Nov 05 2015

Formula

a(n) = Sum_{k=1..A000041(n)} A263003(n,k).

Extensions

a(0)=1 prepended by Alois P. Heinz, Nov 05 2015