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
Links
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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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 *) -
PARI
a(n) = polcoeff(((x^n-1)/(x-1))^9, 2*n-2); \\ Michel Marcus, Feb 17 2016
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.
Extensions
More terms from Robert G. Wilson v, Jul 30 2010