A179097 Rectified heptapeton (6-simplex) numbers: the coefficient of x^(2n-2) in (1+x+x^2+...+x^(n-1))^7.

0, 1, 21, 161, 728, 2415, 6538, 15330, 32292, 62601, 113575, 195195, 320684, 507143, 776244, 1154980, 1676472, 2380833, 3316089, 4539157, 6116880, 8127119, 10659902, 13818630, 17721340, 22502025, 28312011, 35321391, 43720516

Offset

0,3

Links

J. Conrad, Table of n, a(n) for n = 0..53

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

Conjecture: a(n) = n*(40+26*n+5*n^2+75*n^3+75*n^4+19*n^5)/240. G.f.: x*(1+14*x+35*x^2+7*x^3)/(1-x)^7. - Colin Barker, Jan 09 2012

These conjectures are true, see A179095 for proof.

Mathematica

f[n_] := CoefficientList[ Series[ Sum[x^k, {k, 0, n - 1}]^7, {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))^7, 2*n-2); \\ Michel Marcus, Feb 17 2016

Crossrefs

Cf. A179095, A179096, A179098, A179099.

Sequence in context: A108675 A296832 A267473 * A070315 A242191 A146301

Adjacent sequences: A179094 A179095 A179096 * A179098 A179099 A179100

Keyword

nonn,easy

Author

Michael A. Jackson, Jun 29 2010

Extensions

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

Status

approved