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%I #15 Feb 08 2021 13:56:45
%S 1,34,353,2037,8272,26585,72302,173502,377739,760804,1437799,2576795,
%T 4415346,7280131,11609996,17982668,27145413,40049910,57891613,
%U 82153873,114657092,157613181,213685594,286055210,378492335,495435096,642074499,824446423,1049530822
%N Expansion of (1 + 26*x + 109*x^2 + 109*x^3 + 26*x^4 + x^5) / (1 - x)^8.
%H Colin Barker, <a href="/A244881/b244881.txt">Table of n, a(n) for n = 0..1000</a>
%H Rida Ait El Manssour and Anna-Laura Sattelberger, <a href="https://arxiv.org/abs/2102.03182">Combinatorial Differential Algebra of x^p</a>, arXiv:2102.03182 [math.AG], 2021. Mentions this sequence.
%H R. P. Stanley, <a href="/A002721/a002721.pdf">Examples of Magic Labelings</a>, Unpublished Notes, 1973 [Cached copy, with permission]. See page 31.
%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 From _Colin Barker_, Jan 12 2017: (Start)
%F a(n) = (2520 + 11526*n + 22617*n^2 + 24724*n^3 + 16275*n^4 + 6454*n^5 + 1428*n^6 + 136*n^7) / 2520.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.
%F (End)
%o (PARI) Vec((1 + x)*(1 + 25*x + 84*x^2 + 25*x^3 + x^4) / (1 - x)^8 + O(x^30)) \\ _Colin Barker_, Jan 12 2017
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Jul 08 2014
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