A279282 Self-composition of the cubes; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000578.

0, 1, 16, 182, 1720, 14149, 106944, 760463, 5160488, 33756514, 214369376, 1328496947, 8065970016, 48125315989, 282851349184, 1640791635086, 9409099218712, 53408767286521, 300417148670400, 1676056809217283, 9282172245277448, 51062759750186170, 279196558362482192, 1518068927980989575

Offset: 0

Author

Ilya Gutkovskiy, Dec 09 2016

Keywords

• nonn
• easy

Links

• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Cubic Number
• Index entries for linear recurrences with constant coefficients, signature (20,-158,640,-1553,2920,-4806,5700,-6820,5700,-4806,2920,-1553,640,-158,20,-1).

Crossrefs

Cf. A000578, A030267, A030279.

Programs

Mathematica

CoefficientList[Series[x (1 - x)^4 (1 + 4 x + x^2) (1 - 4 x + 29 x^2 - 84 x^3 + 152 x^4 - 84 x^5 + 29 x^6 - 4 x^7 + x^8)/((1 + x^2)^4 (1 - 5 x + x^2)^4), {x, 0, 23}], x]
LinearRecurrence[{20,-158,640,-1553,2920,-4806,5700,-6820,5700,-4806,2920,-1553,640,-158,20,-1},{0,1,16,182,1720,14149,106944,760463,5160488,33756514,214369376,1328496947,8065970016,48125315989,282851349184,1640791635086},30] (* Harvey P. Dale, Sep 27 2024 *)

Formula

G.f.: x*(1 - x)^4*(1 + 4*x + x^2)*(1 - 4*x + 29*x^2 - 84*x^3 + 152*x^4 - 84*x^5 + 29*x^6 - 4*x^7 + x^8)/((1 + x^2)^4*(1 - 5*x + x^2)^4).