A058581 a(n) = (4*n^2 + 2*n - 3)*(2*n - 1)*n/3.

0, 1, 34, 195, 644, 1605, 3366, 6279, 10760, 17289, 26410, 38731, 54924, 75725, 101934, 134415, 174096, 221969, 279090, 346579, 425620, 517461, 623414, 744855, 883224, 1040025, 1216826, 1415259, 1637020, 1883869, 2157630, 2460191, 2793504, 3159585, 3560514

Offset

0,3

Links

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

From Elmo R. Oliveira, Sep 03 2025: (Start)

G.f.: x*(1 + 29*x + 35*x^2 - x^3)/(1 - x)^5.

E.g.f.: x*(3 + 48*x + 48*x^2 + 8*x^3)*exp(x)/3.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). (End)

Mathematica

Table[(4n^2+2n-3)(2n-1)n/3, {n, 0, 40}] (* Harvey P. Dale, Sep 18 2019 *)

Prog

(PARI) a(n)=(4*n^2+2*n-3)*(2*n-1)*n/3 \\ Charles R Greathouse IV, Oct 21 2022
(PARI) concat(0, Vec(-x*(1+29*x+35*x^2-x^3)/(x-1)^5 + O(x^35))) \\ Elmo R. Oliveira, Sep 03 2025

Crossrefs

Sequence in context: A074709 A074900 A302227 * A050263 A020869 A355884

Adjacent sequences: A058578 A058579 A058580 * A058582 A058583 A058584

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 26 2000

Extensions

More terms from Elmo R. Oliveira, Sep 03 2025

Status

approved