A035012 One half of 9-factorial numbers.

1, 11, 220, 6380, 242440, 11394680, 638102080, 41476635200, 3069271004800, 254749493398400, 23436953392652800, 2367132292657932800, 260384552192372608000, 30985761710892340352000, 3966177498994219565056000, 543366317362208080412672000, 79331482334882379740250112000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..325
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A007558, A034171, A035012, A035013, A035017, A035018.

Cf. A035020, A035021, A035022, A035023, A045756, A084949.

Programs

Magma

[n le 1 select 1 else (9*n-7)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022

Mathematica

s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 10, 2*5!, 9}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Table[9^n*Pochhammer[2/9, n]/2, {n, 40}] (* G. C. Greubel, Oct 18 2022 *)

SageMath

[9^n*rising_factorial(2/9,n)/2 for n in range(1,40)] # G. C. Greubel, Oct 18 2022

Formula

2*a(n) = (9*n-7)(!^9) := Product_{j=1..n} (9*j - 7).

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

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

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

a(n) = (9*n-7)*a(n-1). (End)

From Amiram Eldar, Dec 21 2022: (Start)

a(n) = A084949(n)/2.

Sum_{n>=1} 1/a(n) = 2*(e/9^7)^(1/9)*(Gamma(2/9) - Gamma(2/9, 1/9)). (End)