A128043 a(n) = (n^3 + n)*6^n.

12, 360, 6480, 88128, 1010880, 10357632, 97977600, 873400320, 7437339648, 61070837760, 486873649152, 3787601264640, 28864133775360, 216128364576768, 1593927097712640, 11600403939459072, 83448431062548480, 594125746510233600, 4191176291792191488, 29322390689305067520

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (24,-216,864,-1296).

Formula

G.f.: 12*x*(1 + 6*x + 36*x^2)/(1 - 6*x)^4. - Vincenzo Librandi, Feb 22 2013

E.g.f.: 12*exp(6*x)*x*(1 + 9*x + 18*x^2). - Stefano Spezia, Dec 27 2025

Mathematica

Table[(n^3 + n) * 6^n, {n, 30}] (* or *) CoefficientList[Series[12 (1 + 6 x + 36 x^2)/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Prog

(Magma) [(n^3 + n)*6^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
(Python)
print([(n**3 + n)*6**n for n in range(1, 30)]) # Aidan Chen, Dec 25 2025

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Sequence in context: A046969 A074094 A012553 * A012431 A012386 A130213

Adjacent sequences: A128040 A128041 A128042 * A128044 A128045 A128046

Keyword

nonn,easy

Author

Mohammad K. Azarian, May 02 2007

Status

approved