A081896 A sequence related to binomial(n+3, 3).

1, 7, 43, 245, 1328, 6944, 35328, 175872, 860160, 4145152, 19726336, 92864512, 433061888, 2002780160, 9193914368, 41926262784, 190052302848, 856845975552, 3843995729920, 17166984282112, 76347338653696, 338237264494592

Offset

0,2

Comments

Binomial transform of A081895.

3rd binomial transform of binomial(n+3, 3), A000292.

4th 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 (16,-96,256,-256)

Formula

a(n) = 4^n*(n^3 + 33*n^2 + 254*n + 384)/384.

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

E.g.f.: (6 + 18*x + 9*x^2 + x^3)*exp(4*x)/6. - G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{16, -96, 256, -256}, {1, 7, 43, 245}, 50] (* G. C. Greubel, Oct 18 2018 *)
CoefficientList[Series[(1-3x)^3/(1-4x)^4, {x, 0, 30}], x] (* Harvey P. Dale, Nov 30 2021 *)

Prog

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

Crossrefs

Cf. A081897.

Sequence in context: A079925 A126718 A346227 * A363413 A193656 A125344

Adjacent sequences: A081893 A081894 A081895 * A081897 A081898 A081899

Keyword

nonn,easy

Author

Paul Barry, Mar 30 2003

Status

approved