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

0,3

Links

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

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

Example

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

Mathematica

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

Crossrefs

Bisection of A318160 (even part).

Cf. A180281.

Sequence in context: A004314 A338099 A125406 * A182311 A181711 A042940

Adjacent sequences: A318158 A318159 A318160 * A318162 A318163 A318164

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2018

Status

approved