A318161 Number of compositions of 2n into exactly 2n nonnegative parts with largest part n.

1, 1, 18, 195, 1652, 12825, 96030, 705341, 5116200, 36773397, 262462010, 1862790699, 13160496684, 92624149475, 649794035142, 4545979700445, 31727803153232, 220975193536845, 1536191185018770, 10661898343645847, 73890140441316420, 511405029708269529

Offset: 0

Author

Alois P. Heinz, Aug 19 2018

Keywords

• nonn

Examples

			a(2) = 18: 0022, 0112, 0121, 0202, 0211, 0220, 1012, 1021, 1102, 1120, 1201, 1210, 2002, 2011, 2020, 2101, 2110, 2200.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1204

Crossrefs

Bisection of A318160 (even part).

Cf. A180281.

Programs

Mathematica

Flatten[{1, Table[n - 2*n^2 + 2*n*Binomial[3*n - 2, n], {n, 1, 20}]}] (* Vaclav Kotesovec, Sep 20 2019 *)

Formula

a(n) = A180281(2n,n).

For n>0, a(n) = n - 2*n^2 + 2*n*binomial(3*n - 2, n). - Vaclav Kotesovec, Sep 20 2019