A081897 A sequence related to binomial(n+3, 3).

1, 8, 58, 396, 2595, 16500, 102500, 625000, 3753125, 22250000, 130468750, 757812500, 4365234375, 24960937500, 141796875000, 800781250000, 4498291015625, 25146484375000, 139953613281250, 775756835937500

Offset

0,2

Comments

Binomial transform of A081895.

4th binomial transform of binomial(n+3, 3), A000292.

5th binomial transform of (1,3,3,1,0,0,0,0,...).

Links

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

Index entries for linear recurrences with constant coefficients, signature (20,-150,500,-625)

Formula

a(n) = 5^n*(n^3 + 42*n^2 + 407*n + 750)/750.

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

E.g.f.: (6 + 18*x + 9*x^2 + x^3)*exp(5*x)/6. - G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{20, -150, 500, -625}, {1, 8, 58, 396}, 50] (* G. C. Greubel, Oct 18 2018 *)

Prog

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

Crossrefs

Sequence in context: A111585 A055839 A297097 * A125371 A162272 A273584

Adjacent sequences: A081894 A081895 A081896 * A081898 A081899 A081900

Keyword

nonn,easy

Author

Paul Barry, Mar 30 2003

Status

approved