A080422 a(n) = (n+1)*(n+2)*(n+3)*(n+12)*3^n/72.

1, 13, 105, 675, 3780, 19278, 91854, 415530, 1804275, 7577955, 30961359, 123589557, 483611310, 1860043500, 7046907660, 26344593252, 97328636181, 355781149065, 1288173125925, 4623863536215, 16466920464456, 58222325927898, 204499905118650, 713919106104750

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-90,270,-405,243).

Formula

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

For n>4, a(n)=15*a(n-1)-90*a(n-2)+270*a(n-3)-405*a(n-4)+243*a(n-5). - Harvey P. Dale, Oct 22 2011

From G. C. Greubel, Dec 22 2023: (Start)

a(n) = A136158(n+4,4).

E.g.f.: (1/8)*(8 + 80*x + 144*x^2 + 72*x^3 + 9*x^4)*exp(3*x). (End)

From Amiram Eldar, Jan 11 2024: (Start)

Sum_{n>=0} 1/a(n) = 662816499/42350 - 2122848*log(3/2)/55.

Sum_{n>=0} (-1)^n/a(n) = 2135808*log(4/3)/55 - 94614897/8470. (End)

Mathematica

Table[(n + 1) (n + 2) (n + 3) (n + 12) 3^n/72, {n, 0, 30}] (* or *) LinearRecurrence[ {15, -90, 270, -405, 243}, {1, 13, 105, 675, 3780}, 30] (* Harvey P. Dale, Oct 22 2011 *)
CoefficientList[Series[(1 - 2 x) / (1 - 3 x)^5, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)

Prog

(Magma) [(n+1)*(n+2)*(n+3)*(n+12)*3^n/72: n in [0..30]]; // Vincenzo Librandi, Aug 05 2013
(SageMath) [(n+1)*(n+2)*(n+3)*(n+12)*3^(n-3)/8 for n in range(31)] # G. C. Greubel, Dec 22 2023

Crossrefs

T(n, 4) in triangle A080419.

Cf. A136158.

Sequence in context: A316425 A317427 A320204 * A030055 A155636 A055902

Adjacent sequences: A080419 A080420 A080421 * A080423 A080424 A080425

Keyword

nonn,easy

Author

Paul Barry, Feb 19 2003

Status

approved