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A081903 A sequence related to binomial(n+5, 5). 2
1, 10, 85, 660, 4830, 33876, 230030, 1522400, 9866375, 62828750, 394146875, 2440812500, 14944687500, 90590625000, 544242187500, 3243437500000, 19189111328125, 112777832031250, 658804931640625, 3827075195312500 (list; graph; refs; listen; history; text; internal format)
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 * A144639 A233667 A038235

Adjacent sequences:  A081900 A081901 A081902 * A081904 A081905 A081906

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 31 2003

STATUS

approved

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Last modified May 26 17:17 EDT 2019. Contains 323597 sequences. (Running on oeis4.)