A179099 - OEIS

%I #19 Aug 03 2022 07:35:55

%S 0,1,36,414,2598,11385,39303,114387,292743,677556,1446445,2889315,

%T 5459103,9838062,17022474,28428930,46025562,72491859,111410946,

%U 167498452,246872340,357368319,508905705,713908845,987789465,1349495550

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

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).

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

%F This conjecture is true, see A179095 for proof.

%t 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 *)

%o (PARI) a(n) = polcoeff(((x^n-1)/(x-1))^9, 2*n-2); \\ _Michel Marcus_, Feb 17 2016

%Y Cf. A179095, A179096, A179097, A179098.

%K nonn,easy

%O 0,3

%A _Michael A. Jackson_, Jun 29 2010

%E More terms from _Robert G. Wilson v_, Jul 30 2010