A081904 Second binomial transform of binomial(n+6, 6).

1, 9, 60, 344, 1794, 8754, 40636, 181380, 784251, 3302451, 13598280, 54922860, 218131380, 853586100, 3296508840, 12581531064, 47510175861, 177681098205, 658665849636, 2422018974096, 8840103322374, 32044237392726, 115417729279620, 413255236888476, 1471500113899311

Offset: 0

Author

Paul Barry, Mar 31 2003

Keywords

• nonn
• easy

Comments

Binomial transform of A055853 (without leading 0).

3rd binomial transform of (1,6,15,20,15,6,1,0,0,0,...).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (21,-189,945,-2835,5103,-5103, 2187).

Crossrefs

Cf. A000579, A055853, A081905.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^6/(1-3*x)^7)); // G. C. Greubel, Oct 18 2018

Mathematica

LinearRecurrence[{21,-189,945,-2835,5103,-5103,2187}, {1,9,60,344,1794, 8754,40636}, 50] (* G. C. Greubel, Oct 18 2018 *)

PARI

x='x+O('x^30); Vec((1-2*x)^6/(1-3*x)^7) \\ G. C. Greubel, Oct 18 2018

Formula

a(n) = 3^n*(n^6 + 93*n^5 + 3055*n^4 + 44055*n^3 + 282424*n^2 + 720132*n + 524880)/524880.

G.f.: (1 - 2*x)^6/(1 - 3*x)^7.

E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(3*x) / 720. - G. C. Greubel, Oct 18 2018