%I #24 Dec 21 2022 04:45:33

%S 1,11,220,6380,242440,11394680,638102080,41476635200,3069271004800,

%T 254749493398400,23436953392652800,2367132292657932800,

%U 260384552192372608000,30985761710892340352000,3966177498994219565056000,543366317362208080412672000,79331482334882379740250112000

%N One half of 9-factorial numbers.

%H G. C. Greubel, <a href="/A035012/b035012.txt">Table of n, a(n) for n = 1..325</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

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

%F E.g.f.: (-1+(1-9*x)^(-2/9))/2.

%F From _G. C. Greubel_, Oct 18 2022: (Start)

%F a(n) = (1/2) * 9^n * Pochhammer(n, 2/9).

%F a(n) = (9*n-7)*a(n-1). (End)

%F From _Amiram Eldar_, Dec 21 2022: (Start)

%F a(n) = A084949(n)/2.

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

%t s=1;lst={s};Do[s+=n*s;AppendTo[lst, s], {n, 10, 2*5!, 9}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 08 2008 *)

%t Table[9^n*Pochhammer[2/9, n]/2, {n, 40}] (* _G. C. Greubel_, Oct 18 2022 *)

%o (Magma) [n le 1 select 1 else (9*n-7)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 18 2022

%o (SageMath) [9^n*rising_factorial(2/9,n)/2 for n in range(1,40)] # _G. C. Greubel_, Oct 18 2022

%Y Cf. A007558, A034171, A035012, A035013, A035017, A035018.

%Y Cf. A035020, A035021, A035022, A035023, A045756, A084949.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_