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Self-composition of the tetrahedral (or triangular pyramidal) numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000292.
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%I #9 Apr 02 2019 19:18:51

%S 0,1,8,52,304,1650,8492,42000,201356,941367,4310480,19395042,85972228,

%T 376185250,1627518840,6971209090,29595604656,124648174343,

%U 521225809112,2165408553994,8942942384500,36733935375275,150138939637144,610840125062072,2474686297520984,9986301300789540

%N Self-composition of the tetrahedral (or triangular pyramidal) numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000292.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>

%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (20,-174,876,-2885,6708,-11612,15476,-16206,13468,-8894,4632,-1868,564,-120,16,-1).

%F G.f.: x*(1 - x)^12/(1 - 5*x + 6*x^2 - 4*x^3 + x^4)^4.

%t CoefficientList[Series[x (1 - x)^12/(1 - 5 x + 6 x^2 - 4 x^3 + x^4)^4, {x, 0, 25}], x]

%t LinearRecurrence[{20,-174,876,-2885,6708,-11612,15476,-16206,13468,-8894,4632,-1868,564,-120,16,-1},{0,1,8,52,304,1650,8492,42000,201356,941367,4310480,19395042,85972228,376185250,1627518840,6971209090},40] (* _Harvey P. Dale_, Jul 26 2018 *)

%Y Cf. A000292, A030280.

%K nonn,easy

%O 0,3

%A _Ilya Gutkovskiy_, Dec 09 2016