A081902 Third binomial transform of binomial(n+5, 5).

1, 9, 66, 434, 2661, 15525, 87240, 475920, 2534400, 13227520, 67866624, 343105536, 1712390144, 8449622016, 41273524224, 199782039552, 959119884288, 4570314964992, 21629992173568, 101729521631232, 475697692803072, 2212565287436288, 10240198466076672, 47175439742926848

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A081901.

4th 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 (24,-240,1280,-3840,6144,-4096).

Crossrefs

Cf. A000389, A081901, A081903.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^5/(1-4*x)^6)); // G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{24, -240, 1280, -3840, 6144, -4096}, {1, 9, 66, 434, 2661, 15525}, 50] (* G. C. Greubel, Oct 18 2018 *)
CoefficientList[Series[(1-3x)^5/(1-4x)^6,{x,0,30}],x] (* Harvey P. Dale, Apr 01 2023 *)

PARI

x='x+O('x^30); Vec((1-3*x)^5/(1-4*x)^6) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = 4^n*(n^5 + 90*n^4 + 2635*n^3 + 29850*n^2 + 121024*n + 122880)/122880.

G.f.: (1 - 3*x)^5/(1 - 4*x)^6.

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