A227273 Expansion of 1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)).

1, 70, 3321, 135450, 5143341, 188253030, 6755426161, 239789821810, 8459827013781, 297439462109790, 10437310023978201, 365844613023404970, 12815338551339471421, 448752409725746315350, 15710645734163363925441, 549958830422813492568930, 19250283677858902044252261

Offset: 0

Author

Yahia Kahloune, Jul 04 2013

Keywords

• nonn
• easy

Comments

Note that the denominator has 5 tetrahedral numbers: 1, 4, 10, 20, 35.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..645
• Index entries for linear recurrences with constant coefficients, signature (70,-1579,13510,-40000,28000).

Crossrefs

Column k=4 of A080249.

Cf. A080250, A002450, A000292.

Programs

Mathematica

CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 10 x) (1 - 20 x) (1 - 35 x)), {x, 0, 50}], x] (* G. C. Greubel, Oct 02 2017 *)

PARI

Vec(1/((1-x)*(1-4*x)*(1-10*x)*(1-20*x)*(1-35*x)) + O(x^50)) \\ Michel Marcus, May 23 2014

Formula

a(n) = (2736*35^(n+4) - 23715*20^(n+4) + 80104*10^(n+4) - 121125*4^(n+4) + 62000)/1081404000.

Extensions

Typo in a(7) fixed by Colin Barker, May 23 2014