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

1, 4, 86, 3486, 178870, 10388788, 652694106, 43304881124, 2990752400778, 212997373622366, 15542763534960598, 1156764114321375362, 87507330113965391948, 6711208401368504338646, 520758394504342278328914, 40818243590325732399837872, 3227693268242421225516534768

Offset: 0

Author

Alois P. Heinz, Jan 18 2012

Keywords

• nonn

Comments

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

Examples

			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}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Bisection of row n=4 of A204459.

Programs

Maple

b:= proc(n, i, t) option remember;
      `if`(it*(2*i-t+1)/2, 0,
      `if`(n=0, 1, b(n, i-1, t) +`if`(n b(n*(8*n+1), 8*n, 2*n):
seq(a(n), n=0..15);

Mathematica

b[n_, i_, t_] /; it(2i-t+1)/2 = 0; b[0, , ] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[nJean-François Alcover, Dec 07 2020, after Alois P. Heinz *)