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%I #19 Aug 03 2022 07:34:34
%S 0,1,21,161,728,2415,6538,15330,32292,62601,113575,195195,320684,
%T 507143,776244,1154980,1676472,2380833,3316089,4539157,6116880,
%U 8127119,10659902,13818630,17721340,22502025,28312011,35321391,43720516
%N Rectified heptapeton (6-simplex) numbers: the coefficient of x^(2n-2) in (1+x+x^2+...+x^(n-1))^7.
%H J. Conrad, <a href="/A179097/b179097.txt">Table of n, a(n) for n = 0..53</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F 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
%F These conjectures are true, see A179095 for proof.
%t 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 *)
%o (PARI) a(n) = polcoeff(((x^n-1)/(x-1))^7, 2*n-2); \\ _Michel Marcus_, Feb 17 2016
%Y Cf. A179095, A179096, A179098, A179099.
%K nonn,easy
%O 0,3
%A _Michael A. Jackson_, Jun 29 2010
%E More terms from _Robert G. Wilson v_, Jul 30 2010
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