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A035012
One half of 9-factorial numbers.
14
1, 11, 220, 6380, 242440, 11394680, 638102080, 41476635200, 3069271004800, 254749493398400, 23436953392652800, 2367132292657932800, 260384552192372608000, 30985761710892340352000, 3966177498994219565056000, 543366317362208080412672000, 79331482334882379740250112000
OFFSET
1,2
FORMULA
2*a(n) = (9*n-7)(!^9) := Product_{j=1..n} (9*j - 7).
E.g.f.: (-1+(1-9*x)^(-2/9))/2.
From G. C. Greubel, Oct 18 2022: (Start)
a(n) = (1/2) * 9^n * Pochhammer(n, 2/9).
a(n) = (9*n-7)*a(n-1). (End)
From Amiram Eldar, Dec 21 2022: (Start)
a(n) = A084949(n)/2.
Sum_{n>=1} 1/a(n) = 2*(e/9^7)^(1/9)*(Gamma(2/9) - Gamma(2/9, 1/9)). (End)
MATHEMATICA
s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 10, 2*5!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
Table[9^n*Pochhammer[2/9, n]/2, {n, 40}] (* G. C. Greubel, Oct 18 2022 *)
PROG
(Magma) [n le 1 select 1 else (9*n-7)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(2/9, n)/2 for n in range(1, 40)] # G. C. Greubel, Oct 18 2022
KEYWORD
easy,nonn
STATUS
approved