A338337 Coefficient of x^(6*n)*y^(6*n)*z^(6*n) in the expansion of 1/(1-x-y^2-z^3).

1, 4620, 135795660, 5190977391600, 221838126928317900, 10086906430733029017120, 477156732636269771364879600, 23199870600247661786357661924000, 1150983828787218131441395889200471500, 57991163446756752913635026142306805792320, 2957727121295876265116937111814024549631408160

Offset

0,2

Comments

The other diagonal coefficients are zero.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = (11*n)! / ((2*n)! * (3*n)! * (6*n)!). - Vaclav Kotesovec, Oct 28 2020

Maple

a:= proc(n) local h; 1/(1-x-y^2-z^3); for h in [x, y, z]
      do coeff(series(%, h, 1+6*n), h, 6*n) od
    end:
seq(a(n), n=0..10);  # Alois P. Heinz, Oct 23 2020

Mathematica

nmax = 10; Flatten[{1, Table[Coefficient[Series[1/(1 - x - y^2 - z^3), {x, 0, 6*n}, {y, 0, 6*n}, {z, 0, 6*n}], x^(6*n)*y^(6*n)*z^(6*n)], {n, 1, nmax}]}] (* Vaclav Kotesovec, Oct 23 2020 *)

Crossrefs

Cf. A338075, A338076, A338077.

Sequence in context: A253115 A189983 A295431 * A237634 A051649 A140175

Adjacent sequences: A338334 A338335 A338336 * A338338 A338339 A338340

Keyword

nonn

Author

N. J. A. Sloane, Oct 22 2020

Extensions

More terms from Alois P. Heinz, Oct 23 2020

Status

approved