A035020 One sixth of 9-factorial numbers.

1, 15, 360, 11880, 498960, 25446960, 1526817600, 105350414400, 8217332323200, 714907912118400, 68631159563366400, 7206271754153472000, 821514979973495808000, 101046342536739984384000, 13338117214849677938688000, 1880674527293804589355008000, 282101179094070688403251200000

Offset

1,2

Links

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

Index entries for sequences related to factorial numbers.

Formula

6*a(n) = (9*n-3)(!^9) := Product_{j=1..n} (9*j-3) = 3^n*2*A034000(n), where 2*A034000(n) = (3*n-1)(!^3) := Product_{j=1..n} (3*j-1).

E.g.f.: (-1+(1-9*x)^(-2/3))/6.

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

a(n) = (1/6) * 9^n * Pochhammer(n, 2/3).

a(n) = (9*n - 3)*a(n-1). (End)

From Amiram Eldar, Dec 21 2022: (Start)

a(n) = A147630(n+1)/6.

Sum_{n>=1} 1/a(n) = 6*(e/9^3)^(1/9)*(Gamma(2/3) - Gamma(2/3, 1/9)). (End)

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 14, 2*5!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Table[9^n*Pochhammer[2/3, n]/6, {n, 40}] (* G. C. Greubel, Oct 18 2022 *)

Prog

(Magma) [n le 1 select 1 else (9*n-3)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(2/3, n)/6 for n in range(1, 40)] # G. C. Greubel, Oct 18 2022

Crossrefs

Cf. A007559, A034000, A034171, A035012, A035013, A035017, A147630.

Cf. A035018, A035020, A035021, A035022, A035023, A045756.

Sequence in context: A184132 A240197 A012486 * A087330 A035274 A324415

Adjacent sequences: A035017 A035018 A035019 * A035021 A035022 A035023

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved