A035018 One fifth of 9-factorial numbers.

1, 14, 322, 10304, 422464, 21123200, 1246268800, 84746278400, 6525463436800, 561189855564800, 53313036278656000, 5544555772980224000, 626534802346765312000, 76437245886305368064000, 10013279211106003216384000, 1401859089554840450293760000, 208877004343671227093770240000

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

Cf. A035020, A035021, A035022, A035023, A045756, A147629.

Programs

Magma

[n le 1 select 1 else (9*n-4)*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, 13, 2*5!, 9}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Rest[FoldList[Times,1,9*Range[20]-4]/5] (* Harvey P. Dale, May 22 2013 *)

SageMath

[9^n*rising_factorial(5/9,n)/5 for n in range(1,40)] # G. C. Greubel, Oct 18 2022

Formula

5*a(n) = (9*n-4)(!^9) := Product_{j=1..n} (9*j-4).

E.g.f.: (-1+(1-9*x)^(-5/9))/5.

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

a(n) = (1/5) * 9^n * Pochhammer(n, 5/9).

a(n) = (9*n-4)*a(n-1). (End)

From Amiram Eldar, Dec 21 2022: (Start)

a(n) = A147629(n+1)/5.

Sum_{n>=1} 1/a(n) = 5*(e/9^4)^(1/9)*(Gamma(5/9) - Gamma(5/9, 1/9)). (End)