A153647 a(n) = 3^n*(n + 2)!.

2, 18, 216, 3240, 58320, 1224720, 29393280, 793618560, 23808556800, 785682374400, 28284565478400, 1103098053657600, 46330118253619200, 2084855321412864000, 100073055427817472000, 5103725826818691072000, 275601194648209317888000, 15709268094947931119616000

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Dec 30 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A051606.

Programs

Magma

[3^n*Factorial(n + 2): n in [0..20]]; // Vincenzo Librandi, Aug 24 2016

Maple

A153647:= n-> 3^n*(n+2)!; seq(A153647(n), n=0..20); # G. C. Greubel, Mar 03 2021

Mathematica

Table[3^n*(n + 2)!, {n, 0, 30}]

PARI

a(n) = 3^n*(n + 2)!; \\ Michel Marcus, Mar 03 2021

Sage

[3^n*factorial(n+2) for n in (0..20)] # G. C. Greubel, Mar 03 2021

Formula

From G. C. Greubel, Mar 03 2021: (Start)

a(n) = 2*A051606(n).

G.f.: 2*Hypergeometric2F0([1, 3]; --; 3*x).

E.g.f.: 2/(1-3*x)^3. (End)

D-finite with recurrence a(n) + 3*(-n-2)*a(n-1) = 0. - R. J. Mathar, Aug 20 2021

From Amiram Eldar, May 31 2025: (Start)

Sum_{n>=0} 1/a(n) = 9*exp(1/3) - 12.

Sum_{n>=0} (-1)^n/a(n) = 9*exp(-1/3) - 6. (End)