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

0,3

Links

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

Formula

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

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

Crossrefs

Cf. A066183, A117506, A263003.

Sequence in context: A086365 A032270 A198057 * A002750 A178887 A002467

Adjacent sequences: A263001 A263002 A263003 * A263005 A263006 A263007

Keyword

nonn

Author

Wolfdieter Lang, Oct 08 2015

Extensions

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

Status

approved