A081899 A sequence related to binomial(n+4, 4).

1, 8, 54, 332, 1921, 10644, 57072, 298176, 1525248, 7665664, 37953536, 185499648, 896466944, 4289462272, 20343422976, 95718211584, 447146360832, 2075274510336, 9574555844608, 43933220470784, 200579267690496

Offset

0,2

Comments

Binomial transform of A081898.

3rd binomial transform of binomial(n+4, 4), A000332.

4th binomial transform of (1,4,6,4,1,0,0,0,...).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (20,-160,640,-1280,1024).

Formula

a(n) = 4^n*(n^4 + 58*n^3 + 971*n^2 + 5114*n + 6144)/6144.

G.f.: (1 - 3*x)^4/(1 - 4*x)^5.

E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(4*x)/24. - G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{20, -160, 640, -1280, 1024}, {1, 8, 54, 332, 1921}, 50] (* G. C. Greubel, Oct 18 2018 *)

Prog

(PARI) x='x+O('x^30); Vec((1-3*x)^4/(1-4*x)^5) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^4/(1-4*x)^5)); // G. C. Greubel, Oct 18 2018

Crossrefs

Cf. A081900.

Sequence in context: A351845 A037966 A091433 * A057970 A208310 A154235

Adjacent sequences: A081896 A081897 A081898 * A081900 A081901 A081902

Keyword

nonn,easy

Author

Paul Barry, Mar 30 2003

Status

approved