A204462 Number of 2*n-element subsets that can be chosen from {1,2,...,12*n} having element sum n*(12*n+1).

1, 6, 318, 32134, 4083008, 587267282, 91403537276, 15027205920330, 2572042542065646, 454018964549333284, 82122490665668040962, 15150820045467016057500, 2841258381788564812646472, 540201085284535788002286246, 103917818379993516623446237348

Offset: 0

Author

Alois P. Heinz, Jan 18 2012

Keywords

• nonn

Comments

a(n) is the number of partitions of n*(12*n+1) into 2*n distinct parts <=12*n.

Examples

			a(1) = 6 because there are 6 2-element subsets that can be chosen from {1,2,...,12} having element sum 13: {1,12}, {2,11}, {3,10}, {4,9}, {5,8}, {6,7}.
		

Crossrefs

Bisection of row n=6 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*(12*n+1), 12*n, 2*n):
seq(a(n), n=0..12);

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 *)