A081898 Second binomial transform of binomial(n+4, 4).

1, 7, 39, 193, 886, 3858, 16146, 65502, 259119, 1003833, 3820689, 14322663, 52986636, 193759452, 701265924, 2514778812, 8943620589, 31569189723, 110673119691, 385569479997, 1335567565746, 4601780568342, 15778086835014, 53852222811978, 183024799992891, 619577180566893

Offset: 0

Author

Paul Barry, Mar 30 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A055589 (without leading 0).

3rd 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 (15,-90,270,-405,243).

Crossrefs

Cf. A000332, A055589, A081899.

Programs

Magma

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

Mathematica

LinearRecurrence[{15,-90,270,-405,243}, {1,7,39,193,886}, 50] (* G. C. Greubel, Oct 18 2018 *)

PARI

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

Formula

a(n) = 3^n*(n^4 + 42*n^3 + 515*n^2 + 2034*n + 1944)/1944.

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

E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(3*x)/24. - G. C. Greubel, Oct 18 2018