A081900 A sequence related to binomial(n+4, 4).

1, 9, 71, 519, 3606, 24150, 157250, 1001250, 6259375, 38534375, 234140625, 1406640625, 8367187500, 49335937500, 288632812500, 1676757812500, 9678955078125, 55548095703125, 317108154296875, 1801483154296875

Offset

0,2

Comments

Binomial transform of A081899.

4th binomial transform of binomial(n+4, 4), A000332.

5th 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 (25,-250,1250,-3125,3125).

Formula

a(n) = 5^n*(n^4 + 74*n^3 + 1571*n^2 + 10354*n + 15000)/15000.

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

E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(5*x)/24. - G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{25, -250, 1250, -3125, 3125}, {1, 9, 71, 519, 3606}, 50] (* G. C. Greubel, Oct 18 2018 *)

Prog

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

Crossrefs

Sequence in context: A226846 A226711 A231420 * A164551 A178869 A057080

Adjacent sequences: A081897 A081898 A081899 * A081901 A081902 A081903

Keyword

nonn,easy

Author

Paul Barry, Mar 31 2003

Status

approved