A035013 One third of 9-factorial numbers.

1, 12, 252, 7560, 294840, 14152320, 806682240, 53241027840, 3993077088000, 335418475392000, 31193918211456000, 3181779657568512000, 353177541990104832000, 42381305038812579840000, 5467188350006822799360000, 754471992300941546311680000, 110907382868238407307816960000, 17301551727445191540019445760000

Offset

1,2

Comments

E.g.f. is g.f. for A034171(n-1).

Links

G. C. Greubel, Table of n, a(n) for n = 1..325

Index entries for sequences related to factorial numbers.

Formula

3*a(n) = (9*n-6)(!^9) := Product_{j=1..n} (9*j-6) = 3^n*A007559(n).

E.g.f.: (-1+(1-9*x)^(-1/3))/3.

From G. C. Greubel, Oct 18 2022: (Start)

a(n) = (1/3) * 9^n * Pochhammer(n, 1/3).

a(n) = (9*n-6)*a(n-1). (End)

From Amiram Eldar, Dec 21 2022: (Start)

a(n) = A144758(n)/3.

Sum_{n>=1} 1/a(n) = 3*(e/9^6)^(1/9)*(Gamma(1/3) - Gamma(1/3, 1/9)). (End)

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 11, 2*5!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Table[9^n*Pochhammer[1/3, n]/3, {n, 40}] (* G. C. Greubel, Oct 18 2022 *)

Prog

(Magma) [n le 1 select 1 else (9*n-6)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(1/3, n)/3 for n in range(1, 40)] # G. C. Greubel, Oct 18 2022

Crossrefs

Cf. A007559, A034171, A035012, A035013, A035017, A035018.

Cf. A035020, A035021, A035022, A035023, A045756, A144758.

Sequence in context: A099139 A289565 A198475 * A382044 A065583 A129585

Adjacent sequences: A035010 A035011 A035012 * A035014 A035015 A035016

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

Terms a(15) onward added by G. C. Greubel, Oct 18 2022

Status

approved