A204461 Number of n-element subsets that can be chosen from {1,2,...,5*n} having element sum n*(5*n+1)/2.

1, 1, 5, 25, 177, 1394, 11963, 108108, 1016737, 9853759, 97809616, 989878326, 10180316707, 106124695130, 1119148085092, 11920389375524, 128077285062639, 1386689101261013, 15115933170815361, 165776800325379769, 1828006462946421194, 20256667860779557632

Offset: 0

Author

Alois P. Heinz, Jan 18 2012

Keywords

• nonn

Comments

a(n) is the number of partitions of n*(5*n+1)/2 into n distinct parts <=5*n.

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100

Crossrefs

Row n=5 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*(5*n+1)/2, 5*n, n):
seq(a(n), n=0..20);

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 *)