A147626 Octo-factorial numbers (5).

1, 6, 84, 1848, 55440, 2106720, 96909120, 5233092480, 324451733760, 22711621363200, 1771506466329600, 152349556104345600, 14320858273808486400, 1460727543928465612800, 160680029832131217408000, 18960243520191483654144000, 2388990683544126940422144000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..325

Formula

a(n+1) = Sum_{k=0..n} A132393(n,k)*6^k*8^(n-k). - Philippe Deléham, Nov 09 2008

a(n) = (-2)^n*Sum_{k=0..n} 4^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012

G.f.: 2*x/G(0), where G(k) = 1 + 1/(1 - 2*x*(8*k+6)/(2*x*(8*k+6) - 1 + 16*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013

From G. C. Greubel, Oct 21 2022: (Start)

a(n) = 8^n * Pochhammer(n, 3/4) = -2^(3*n-1) * Pochhammer(n, -1/4).

a(n) = (8*n - 10)*a(n-1). (End)

Sum_{n>=1} 1/a(n) = 1 + (e/8^2)^(1/8)*(Gamma(3/4) - Gamma(3/4, 1/8)). - Amiram Eldar, Dec 20 2022

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 2*5!, 8}]; lst
Table[8^(n-1)*Pochhammer[3/4, n-1], {n, 40}] (* G. C. Greubel, Oct 21 2022 *)

Prog

(Magma) [n le 1 select 1 else (8*n-10)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 21 2022
(SageMath) [8^(n-1)*rising_factorial(3/4, n-1) for n in range(1, 40)] # G. C. Greubel, Oct 21 2022

Crossrefs

Cf. A034908, A045755, A048994, A049210, A051189, A052714, A132393, A147625.

Sequence in context: A369531 A322518 A014062 * A123312 A010794 A177560

Adjacent sequences: A147623 A147624 A147625 * A147627 A147628 A147629

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Status

approved