A081903 Fourth binomial transform of binomial(n+5, 5).

1, 10, 85, 660, 4830, 33876, 230030, 1522400, 9866375, 62828750, 394146875, 2440812500, 14944687500, 90590625000, 544242187500, 3243437500000, 19189111328125, 112777832031250, 658804931640625, 3827075195312500, 22117736816406250, 127216186523437500, 728480529785156250

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A081902.

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).

Crossrefs

Cf. A000389, A081902.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^5/(1-5*x)^6)); // 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 *)

PARI

my(x='x+O('x^30)); Vec((1-4*x)^5/(1-5*x)^6) \\ G. C. Greubel, Oct 18 2018

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