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A204460 Number of 2*n-element subsets that can be chosen from {1,2,...,8*n} having element sum n*(8*n+1).

%I A204460 #13 Dec 07 2020 02:07:33
%S A204460 1,4,86,3486,178870,10388788,652694106,43304881124,2990752400778,
%T A204460 212997373622366,15542763534960598,1156764114321375362,
%U A204460 87507330113965391948,6711208401368504338646,520758394504342278328914,40818243590325732399837872,3227693268242421225516534768
%N A204460 Number of 2*n-element subsets that can be chosen from {1,2,...,8*n} having element sum n*(8*n+1).
%C A204460 a(n) is the number of partitions of n*(8*n+1) into 2*n distinct parts <=8*n.
%H A204460 Alois P. Heinz, <a href="/A204460/b204460.txt">Table of n, a(n) for n = 0..50</a>
%e A204460 a(1) = 4 because there are 4 2-element subsets that can be chosen from {1,2,...,8} having element sum 9: {1,8}, {2,7}, {3,6}, {4,5}.
%p A204460 b:= proc(n, i, t) option remember;
%p A204460       `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,
%p A204460       `if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))
%p A204460     end:
%p A204460 a:= n-> b(n*(8*n+1), 8*n, 2*n):
%p A204460 seq(a(n), n=0..15);
%t A204460 b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;
%t A204460 b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]];
%t A204460 a[n_] := b[n(8n+1), 8n, 2n];
%t A204460 a /@ Range[0, 15] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A204460 Bisection of row n=4 of A204459.
%K A204460 nonn
%O A204460 0,2
%A A204460 _Alois P. Heinz_, Jan 18 2012