OFFSET
1,2
LINKS
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved