A179096 Rectified hexateron (5-simplex) numbers: the coefficient of x^(2n-2) in (1+x+x^2+...+x^(n-1))^6.

0, 1, 15, 90, 336, 951, 2247, 4676, 8856, 15597, 25927, 41118, 62712, 92547, 132783, 185928, 254864, 342873, 453663, 591394, 760704, 966735, 1215159, 1512204, 1864680, 2280005, 2766231, 3332070, 3986920, 4740891, 5604831, 6590352

Offset

0,3

Comments

a(n) is the number of ordered 6-tuples (j_1,...,j_6) with 0 <= j_i <= n-1 and Sum_{i=1..6} j_i = 2n-2. - Robert Israel, Feb 17 2016

Links

J. Conrad and Robert Israel, Table of n, a(n) for n = 0..1000 (n = 0..98 from J. Conrad)

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

Conjectures: a(n) = n*(n+1)*(13*n^3+12*n^2-7*n+12)/60. G.f.: x*(1+9*x+x^3+15*x^2)/(x-1)^6. - R. J. Mathar, Jul 06 2010

These conjectures are true, see A179095 for proof.

Maple

F:= n -> coeff(add(x^i, i=0..n-1)^6, x, 2*n-2):
seq(F(n), n=0..100); # Robert Israel, Feb 17 2016

Mathematica

f[n_] := CoefficientList[ Series[ Sum[x^k, {k, 0, n - 1}]^6, {x, 0, 2 n + 3}], x][[2 n - 1]]; Array[f, 36] (* Robert G. Wilson v, Jul 30 2010 *)

Prog

(PARI) a(n) = polcoeff(((x^n-1)/(x-1))^6, 2*n-2); \\ Michel Marcus, Feb 17 2016

Crossrefs

Cf. A179095, A179097, A179098, A179099.

Sequence in context: A022707 A323334 A151974 * A328994 A001297 A005716

Adjacent sequences: A179093 A179094 A179095 * A179097 A179098 A179099

Keyword

nonn,easy

Author

Michael A. Jackson, Jun 29 2010

Status

approved