OFFSET
1,2
LINKS
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)
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 *)
PROG
(Magma) [n le 1 select 1 else (9*n-4)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(5/9, n)/5 for n in range(1, 40)] # G. C. Greubel, Oct 18 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved