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%I #17 Aug 03 2022 07:35:11
%S 0,1,28,266,1428,5475,16808,44052,102552,217701,429220,796510,1405196,
%T 2374983,3868944,6104360,9365232,14016585,20520684,29455282,41534020,
%U 57629099,78796344,106302780,141656840,186641325,243349236,314222598
%N Rectified 7-simplex number: the coefficient of x^(2n-2) in (1+x+x^2+...+x^(n-1))^8.
%H J. Conrad, <a href="/A179098/b179098.txt">Table of n, a(n) for n = 0..34</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F Conjectures: a(n) = n*(90+77*n+140*n^3+210*n^4+98*n^5+15*n^6)/630. G.f.: x*(1+20*x+70*x^2+28*x^3+x^4)/(1-x)^8. - _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}]^8, {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))^8, 2*n-2); \\ _Michel Marcus_, Feb 17 2016
%Y Cf. A179095, A179096, A179097, A179099.
%K nonn
%O 0,3
%A _Michael A. Jackson_, Jun 29 2010
%E More terms from _Robert G. Wilson v_, Jul 30 2010