A204466 Number of 2*n-element subsets that can be chosen from {1,2,...,20*n} having element sum n*(20*n+1).

1, 10, 1588, 479632, 181913856, 78132541528, 36324664278320, 17841778519299678, 9124496750611111054, 4812920777714763364122, 2601500672087054002816858, 1434306387533099461310390376, 803846503605741741601245431730, 456755915371658053029595187998278

Offset

0,2

Comments

a(n) is the number of partitions of n*(20*n+1) into 2*n distinct parts <=20*n.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..30

Example

a(1) = 10 because there are 10 2-element subsets that can be chosen from {1,2,...,20} having element sum 21: {1,20}, {2,19}, {3,18}, {4,17}, {5,16}, {6,15}, {7,14}, {8,13}, {9,12}, {10,11}.

Maple

b:= proc(n, i, t) option remember;
      `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,
      `if`(n=0, 1, b(n, i-1, t) +`if`(n<i, 0, b(n-i, i-1, t-1))))
    end:
a:= n-> b(n*(20*n+1), 20*n, 2*n):
seq(a(n), n=0..10);

Mathematica

b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]];
a[n_] := b[n(20n+1), 20n, 2n];
a /@ Range[0, 10] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)

Crossrefs

Bisection of row n=10 of A204459.

Sequence in context: A172958 A286397 A160236 * A117523 A203696 A203530

Adjacent sequences: A204463 A204464 A204465 * A204467 A204468 A204469

Keyword

nonn

Author

Alois P. Heinz, Jan 18 2012

Status

approved