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%I #7 Apr 02 2019 19:18:57
%S 0,1,10,74,469,2662,14115,71360,348143,1652200,7669883,34969286,
%T 157060011,696514465,3055404733,13277356490,57222978070,244831062184,
%U 1040760406476,4398642943496,18493603597214,77388169532299,322451025667910,1338291853544522,5534486308363461,22812231761335189,93741611639348947,384122032722040412
%N Self-composition of the pentagonal numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000326.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (12,-51,91,-75,66,-28,15,-3,1).
%F G.f.: x*(1 - x)^3*(1 + 2*x)*(1 - x + 7*x^2 - x^3)/(1 - 4*x + x^2 - x^3)^3.
%F a(n) = 12*a(n-1) - 51*a(n-2) + 91*a(n-3) - 75*a(n-4) + 66*a(n-5) - 28*a(n-6) + 15*a(n-7) - 3*a(n-8) + a(n-9).
%t CoefficientList[Series[x (1 - x)^3 (1 + 2 x) (1 - x + 7 x^2 - x^3)/(1 - 4 x + x^2 - x^3)^3, {x, 0, 25}], x]
%t LinearRecurrence[{12, -51, 91, -75, 66, -28, 15, -3, 1}, {0, 1, 10, 74, 469, 2662, 14115, 71360, 348143}, 26]
%Y Cf. A000326, A030279, A030280.
%K nonn,easy
%O 0,3
%A _Ilya Gutkovskiy_, Dec 09 2016
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