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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). 2

%I

%S 1,4,86,3486,178870,10388788,652694106,43304881124,2990752400778,

%T 212997373622366,15542763534960598,1156764114321375362,

%U 87507330113965391948,6711208401368504338646,520758394504342278328914,40818243590325732399837872,3227693268242421225516534768

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

%C a(n) is the number of partitions of n*(8*n+1) into 2*n distinct parts <=8*n.

%H Alois P. Heinz, <a href="/A204460/b204460.txt">Table of n, a(n) for n = 0..50</a>

%e 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 b:= proc(n, i, t) option remember;

%p `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,

%p `if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))

%p end:

%p a:= n-> b(n*(8*n+1), 8*n, 2*n):

%p seq(a(n), n=0..15);

%t b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;

%t 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 a[n_] := b[n(8n+1), 8n, 2n];

%t a /@ Range[0, 15] (* _Jean-Fran├žois Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)

%Y Bisection of row n=4 of A204459.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jan 18 2012

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Last modified October 17 21:17 EDT 2021. Contains 348065 sequences. (Running on oeis4.)