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One third of octo-factorial numbers.
7

%I #30 Dec 20 2022 03:51:17

%S 1,11,209,5643,197505,8492715,433128465,25554579435,1712156822145,

%T 128411761660875,10658176217852625,969894035824588875,

%U 96019509546634298625,10274087521489869952875,1181520064971335044580625,145326967991474210483416875,19037832806883121573327610625

%N One third of octo-factorial numbers.

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

%F 3*a(n) = (8*n-5)(!^8) = product(8*j-5, j=1..n).

%F E.g.f.: (-1+(1-8*x)^(-3/8))/3.

%F G.f.: x/(1-11x/(1-8x/(1-19x/(1-16x/(1-27x/(1-24x/(1-35x/(1-32x/(1-... (continued fraction). - _Philippe Deléham_, Jan 07 2012

%F From _Amiram Eldar_, Dec 20 2022: (Start)

%F a(n) = A144756(n)/3.

%F Sum_{n>=1} 1/a(n) = 3*(e/8^5)^(1/8)*(Gamma(3/8) - Gamma(3/8, 1/8)). (End)

%Y Cf. A045755, A034908, A034909, A034910, A034911, A034912, A144756.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_