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

%I A263004 #18 Feb 27 2018 18:56:48
%S A263004 1,1,4,15,76,368,2365,14892,116236,966064,9256889,96638496,1129309316,
%T A263004 14261533248,196315312964,2900635720869,45926240752560,
%U A263004 773725147192412,13831256551416480,261227089570409028,5198858467673903360,108706624576630569271
%N A263004 Row sums of the partition array for the products of the hook lengths numbers of Ferrers (or Young) diagrams A263003.
%H A263004 Alois P. Heinz, <a href="/A263004/b263004.txt">Table of n, a(n) for n = 0..60</a>
%F A263004 a(n) = Sum_{k=1..A000041(n)} A263003(n,k).
%p A263004 h:= l-> (n-> mul(mul(1+l[i]-j+add(`if`(l[k]>=j, 1, 0),
%p A263004              k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):
%p A263004 g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), `if`(i<1, 0,
%p A263004                 `if`(i>n, 0, g(n-i, i, [l[], i]))+g(n, i-1, l))):
%p A263004 a:= n-> g(n$2, []):
%p A263004 seq(a(n), n=0..22);  # _Alois P. Heinz_, Nov 05 2015
%Y A263004 Cf. A066183, A117506, A263003.
%K A263004 nonn
%O A263004 0,3
%A A263004 _Wolfdieter Lang_, Oct 08 2015
%E A263004 a(0)=1 prepended by _Alois P. Heinz_, Nov 05 2015