cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Michael A. Jackson, Jun 29 2010

Keywords

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

Crossrefs

Programs

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

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.