A179098 Rectified 7-simplex number: the coefficient of x^(2n-2) in (1+x+x^2+...+x^(n-1))^8.

0, 1, 28, 266, 1428, 5475, 16808, 44052, 102552, 217701, 429220, 796510, 1405196, 2374983, 3868944, 6104360, 9365232, 14016585, 20520684, 29455282, 41534020, 57629099, 78796344, 106302780, 141656840, 186641325, 243349236, 314222598

Offset: 0

Author

Michael A. Jackson, Jun 29 2010

Keywords

• nonn

Links

• J. Conrad, Table of n, a(n) for n = 0..34
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A179095, A179096, A179097, A179099.

Programs

Mathematica

f[n_] := CoefficientList[ Series[ Sum[ x^k, {k, 0, n - 1}]^8, {x, 0, 2 n + 3}], x][[2 n - 1]]; Array[f, 33] (* Robert G. Wilson v, Jul 30 2010 *)

PARI

a(n) = polcoeff(((x^n-1)/(x-1))^8, 2*n-2); \\ Michel Marcus, Feb 17 2016

Formula

Conjectures: a(n) = n*(90+77*n+140*n^3+210*n^4+98*n^5+15*n^6)/630. G.f.: x*(1+20*x+70*x^2+28*x^3+x^4)/(1-x)^8. - Colin Barker, Jan 09 2012

These conjectures are true, see A179095 for proof.

Extensions

More terms from Robert G. Wilson v, Jul 30 2010