A279283 Self-composition of the tetrahedral (or triangular pyramidal) numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000292.

0, 1, 8, 52, 304, 1650, 8492, 42000, 201356, 941367, 4310480, 19395042, 85972228, 376185250, 1627518840, 6971209090, 29595604656, 124648174343, 521225809112, 2165408553994, 8942942384500, 36733935375275, 150138939637144, 610840125062072, 2474686297520984, 9986301300789540

Offset: 0

Author

Ilya Gutkovskiy, Dec 09 2016

Keywords

• nonn
• easy

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index to sequences related to pyramidal numbers
• Index entries for linear recurrences with constant coefficients, signature (20,-174,876,-2885,6708,-11612,15476,-16206,13468,-8894,4632,-1868,564,-120,16,-1).

Crossrefs

Cf. A000292, A030280.

Programs

Mathematica

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

Formula

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