A035022 One eighth of 9-factorial numbers.

1, 17, 442, 15470, 680680, 36076040, 2236714480, 158806728080, 12704538246400, 1130703903929600, 110808982585100800, 11856561136605785600, 1375361091846271129600, 171920136480783891200000, 23037298288425041420800000, 3294333655244780923174400000, 500738715597206700322508800000

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

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

a(n) = (9*n)!/(n!*2^4*3^(4*n)*5*7*A045756(n)*A035012(n)*A007559(n)*A035017(n) *A035018(n)*A034000(n) *A035021(n)).

E.g.f.: (-1+(1-9*x)^(-8/9))/8.

D-finite with recurrence: a(1) = 1, a(n) = (9*n - 1)*a(n-1) for n > 1. - Georg Fischer, Feb 15 2020

a(n) = (1/8) * 9^n * Pochhammer(n, 8/9). - G. C. Greubel, Oct 19 2022

From Amiram Eldar, Dec 21 2022: (Start)

a(n) = A049211(n)/8.

Sum_{n>=1} 1/a(n) = 8*(e/9)^(1/9)*(Gamma(8/9) - Gamma(8/9, 1/9)). (End)

Maple

f := gfun:-rectoproc({(9*n - 1)*a(n - 1) - a(n) = 0, a(1) = 1}, a(n), remember);
map(f, [$ (1 .. 20)]); # Georg Fischer, Feb 15 2020

Mathematica

Table[9^n*Pochhammer[8/9, n]/8, {n, 40}] (* G. C. Greubel, Oct 19 2022 *)

Prog

(Magma) [n le 1 select 1 else (9*n-1)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 19 2022
(SageMath) [9^n*rising_factorial(8/9, n)/8 for n in range(1, 40)] # G. C. Greubel, Oct 19 2022

Crossrefs

Cf. A007559, A034000, A034171, A035012, A035013, A035017, A049211.

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

Sequence in context: A158063 A370543 A301642 * A012117 A271438 A371488

Adjacent sequences: A035019 A035020 A035021 * A035023 A035024 A035025

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved