A081903 A sequence related to binomial(n+5, 5).

1, 10, 85, 660, 4830, 33876, 230030, 1522400, 9866375, 62828750, 394146875, 2440812500, 14944687500, 90590625000, 544242187500, 3243437500000, 19189111328125, 112777832031250, 658804931640625, 3827075195312500

Offset

0,2

Comments

Binomial transform of A081902.

4th binomial transform of binomial(n+5, 5).

5th binomial transform of (1,5,10,10,5,1,0,0,0,...).

Links

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

Index entries for linear recurrences with constant coefficients, signature (30,-375,2500,-9375,18750,-15625).

Formula

a(n) = 5^n*(n^5 + 115*n^4 + 4285*n^3 + 61325*n^2 + 309274*n + 375000)/375000.

G.f.: (1 - 4*x)^5/(1 - 5*x)^6.

E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(5*x)/120. - G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{30, -375, 2500, -9375, 18750, -15625}, {1, 10, 85, 660, 4830, 33876}, 30] (* Harvey P. Dale, Sep 27 2018 *)

Prog

(PARI) x='x+O('x^30); Vec((1-4*x)^5/(1-5*x)^6) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^5/(1-5*x)^6); // G. C. Greubel, Oct 18 2018

Crossrefs

Sequence in context: A323970 A253009 A291389 * A346319 A361285 A144639

Adjacent sequences: A081900 A081901 A081902 * A081904 A081905 A081906

Keyword

nonn,easy

Author

Paul Barry, Mar 31 2003

Status

approved