A318162 Number of compositions of 2n-1 into exactly 2n-1 nonnegative parts with largest part n.

1, 6, 50, 392, 2970, 22022, 160888, 1162800, 8335338, 59366450, 420630210, 2967563040, 20861295000, 146203657992, 1021964428880, 7127260128736, 49606676100234, 344658278690250, 2390849931605590, 16561583202364200, 114577083158683530, 791757148201073670

Offset: 1

Author

Alois P. Heinz, Aug 19 2018

Keywords

• nonn

Examples

			a(1) = 1: 1.
a(2) = 6: 012, 021, 102, 120, 201, 210.
a(3) = 50: 00023, 00032, 00113, 00131, 00203, 00230, 00302, 00311, 00320, 01013, 01031, 01103, 01130, 01301, 01310, 02003, 02030, 02300, 03002, 03011, 03020, 03101, 03110, 03200, 10013, 10031, 10103, 10130, 10301, 10310, 11003, 11030, 11300, 13001, 13010, 13100, 20003, 20030, 20300, 23000, 30002, 30011, 30020, 30101, 30110, 30200, 31001, 31010, 31100, 32000.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1205

Crossrefs

Bisection of A318160 (odd part).

Cf. A180281.

Programs

Maple

a:= proc(n) option remember; (2*n-1)*`if`(n<3, n,
      3*(3*n-4)*(3*n-5)*a(n-1)/(2*(n-1)*(2*n-3)^2))
    end:
seq(a(n), n=1..30);

Mathematica

Flatten[{1, Table[2*(2*n - 1)*Binomial[3*n - 4, n-2], {n, 2, 20}]}] (* Vaclav Kotesovec, Sep 20 2019 *)

Formula

a(n) = A180281(2n-1,n).

For n>1, a(n) = 2*(2*n - 1) * binomial(3*n - 4, n-2). - Vaclav Kotesovec, Sep 20 2019