A080423 a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360.

1, 16, 153, 1134, 7182, 40824, 214326, 1058508, 4979799, 22517352, 98513415, 419129802, 1741000716, 7083045648, 28296044604, 111232727064, 431026817373, 1648861601184, 6234757929477, 23328137324646, 86451332438394, 317576323243080, 1157228874847890, 4185605730648420

Offset: 0

Author

Paul Barry, Feb 19 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (18,-135,540,-1215,1458,-729).

Crossrefs

T(n, 5) of triangle A080419.

Cf. A136158.

Programs

Magma

[(n+1)*(n+2)*(n+3)*(n+4)*(n+15)*3^n/360: n in [0..30]]; // Vincenzo Librandi, Aug 05 2013

Mathematica

CoefficientList[Series[(1 - 2 x) / (1 - 3 x)^6, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
Table[3^n*(n+15)*Binomial[n+4,4]/15, {n,0,30}] (* G. C. Greubel, Dec 22 2023 *)

SageMath

[3^n*(n+15)*binomial(n+4,4)/15 for n in range(31)] # G. C. Greubel, Dec 22 2023

Formula

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

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

a(n) = A136158(n+5, 5).

E.g.f.: (1/40)*(40 + 520*x + 1320*x^2 + 1080*x^3 + 315*x^4 + 27*x^5)*exp(3*x). (End)

From Amiram Eldar, Jan 11 2024: (Start)

Sum_{n>=0} 1/a(n) = 215084880*log(3/2)/1001 - 99766344351/1145144.

Sum_{n>=0} (-1)^n/a(n) = 216218880*log(4/3)/1001 - 498108421095/8016008. (End)