A035021 One seventh of 9-factorial numbers.

1, 16, 400, 13600, 584800, 30409600, 1854985600, 129848992000, 10258070368000, 902710192384000, 87562888661248000, 9281666198092288000, 1067391612780613120000, 132356559984796026880000, 17603422477977871575040000, 2499685991872857763655680000, 377452584772801522312007680000

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

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

E.g.f.: (-1+(1-9*x)^(-7/9))/7.

D-finite with recurrence: a(1) = 1, a(n) = (9*n - 2)*a(n-1) for n > 1. - Georg Fischer, Feb 15 2020

a(n) = (1/7) * 9^n * Pochhammer(n, 7/9). - G. C. Greubel, Oct 19 2022

From Amiram Eldar, Dec 21 2022: (Start)

a(n) = A147631(n+1)/7.

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

Maple

f := gfun:-rectoproc({(9*n - 2)*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[7/9, n]/7, {n, 40}] (* G. C. Greubel, Oct 19 2022 *)

Prog

(Magma) [n le 1 select 1 else (9*n-2)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 19 2022
(SageMath) [9^n*rising_factorial(7/9, n)/7 for n in range(1, 40)] # G. C. Greubel, Oct 19 2022

Crossrefs

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

Cf. A035020, A035021, A035022, A035023, A045756, A147631.

Sequence in context: A269643 A071133 A186854 * A300469 A326102 A300808

Adjacent sequences: A035018 A035019 A035020 * A035022 A035023 A035024

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

Terms a(15) onward added by G. C. Greubel, Oct 19 2022

Status

approved