A081894 Fourth binomial transform of C(n+2,2).

1, 7, 46, 290, 1775, 10625, 62500, 362500, 2078125, 11796875, 66406250, 371093750, 2060546875, 11376953125, 62500000000, 341796875000, 1861572265625, 10101318359375, 54626464843750, 294494628906250, 1583099365234375

Offset: 0

Author

Paul Barry, Mar 30 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A081893.

4th binomial transform of C(n+2,2), A000217.

5th binomial transform of (1,2,1,0,0,0,.....)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (15,-75,125).

Crossrefs

Cf. A081907.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^2/(1-5*x)^3)); // G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{15, -75, 125}, {1, 7, 46}, 50] (* G. C. Greubel, Oct 18 2018 *)

PARI

x='x+O('x^30); Vec((1-4*x)^2/(1-5*x)^3) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = 5^n*(n^2 + 19*n + 50)/50.

G.f.: (1 - 4*x)^2/(1 - 5*x)^3.

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