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Row sums of the partition array for the products of the hook lengths numbers of Ferrers (or Young) diagrams A263003.
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%I #18 Feb 27 2018 18:56:48

%S 1,1,4,15,76,368,2365,14892,116236,966064,9256889,96638496,1129309316,

%T 14261533248,196315312964,2900635720869,45926240752560,

%U 773725147192412,13831256551416480,261227089570409028,5198858467673903360,108706624576630569271

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

%H Alois P. Heinz, <a href="/A263004/b263004.txt">Table of n, a(n) for n = 0..60</a>

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

%p h:= l-> (n-> mul(mul(1+l[i]-j+add(`if`(l[k]>=j, 1, 0),

%p k=i+1..n), j=1..l[i]), i=1..n))(nops(l)):

%p g:= (n, i, l)-> `if`(n=0 or i=1, h([l[], 1$n]), `if`(i<1, 0,

%p `if`(i>n, 0, g(n-i, i, [l[], i]))+g(n, i-1, l))):

%p a:= n-> g(n$2, []):

%p seq(a(n), n=0..22); # _Alois P. Heinz_, Nov 05 2015

%Y Cf. A066183, A117506, A263003.

%K nonn

%O 0,3

%A _Wolfdieter Lang_, Oct 08 2015

%E a(0)=1 prepended by _Alois P. Heinz_, Nov 05 2015