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

1,2

Links

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

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

Example

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.

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 *)

Crossrefs

Bisection of A318160 (odd part).

Cf. A180281.

Sequence in context: A223816 A180880 A308860 * A027330 A090409 A212233

Adjacent sequences: A318159 A318160 A318161 * A318163 A318164 A318165

Keyword

nonn

Author

Alois P. Heinz, Aug 19 2018

Status

approved