A081900 Fourth binomial transform of binomial(n+4, 4).

1, 9, 71, 519, 3606, 24150, 157250, 1001250, 6259375, 38534375, 234140625, 1406640625, 8367187500, 49335937500, 288632812500, 1676757812500, 9678955078125, 55548095703125, 317108154296875, 1801483154296875, 10188293457031250, 57380676269531250, 321922302246093750

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A081899.

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).

Crossrefs

Cf. A000332, A081899.

Programs

Magma

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

PARI

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

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