A179099 Rectified 8-simplex numbers: the coefficient of x^(2n-2) in (1+x+x^2+...+x^(n-1))^9.

0, 1, 36, 414, 2598, 11385, 39303, 114387, 292743, 677556, 1446445, 2889315, 5459103, 9838062, 17022474, 28428930, 46025562, 72491859, 111410946, 167498452, 246872340, 357368319, 508905705, 713908845, 987789465, 1349495550

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

Empirical G.f.: x*(1+27*x+126*x^2+84*x^3+9*x^4)/(1-x)^9. - Colin Barker, Jun 20 2012

This conjecture is true, see A179095 for proof.

Mathematica

f[n_] := CoefficientList[ Series[ Sum[ x^k, {k, 0, n - 1}]^9, {x, 0, 2 n + 3}], x][[2 n - 1]]; Array[f, 33] (* Robert G. Wilson v, Jul 30 2010 *)

Prog

(PARI) a(n) = polcoeff(((x^n-1)/(x-1))^9, 2*n-2); \\ Michel Marcus, Feb 17 2016

Crossrefs

Cf. A179095, A179096, A179097, A179098.

Sequence in context: A055862 A105095 A027782 * A181685 A183353 A178690

Adjacent sequences: A179096 A179097 A179098 * A179100 A179101 A179102

Keyword

nonn,easy

Author

Michael A. Jackson, Jun 29 2010

Extensions

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

Status

approved