A081904 A sequence related to 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

Offset

0,2

Comments

Binomial transform of A055853.

2nd binomial transform of binomial(n+6, 6).

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).

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

Mathematica

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

Prog

(PARI) x='x+O('x^30); Vec((1-2*x)^6/(1-3*x)^7) \\ G. C. Greubel, Oct 18 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^6/(1-3*x)^7)); // G. C. Greubel, Oct 18 2018

Crossrefs

Cf. A081905.

Sequence in context: A288962 A074431 A268965 * A085373 A241976 A082150

Adjacent sequences: A081901 A081902 A081903 * A081905 A081906 A081907

Keyword

nonn,easy

Author

Paul Barry, Mar 31 2003

Status

approved