A147625 Octo-factorial numbers (4).

1, 5, 65, 1365, 39585, 1464645, 65909025, 3493178325, 213083877825, 14702787569925, 1132114642884225, 96229744645159125, 8949366251999798625, 903885991451979661125, 98523573068265783062625, 11527258048987096618327125, 1440907256123387077290890625

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..330

Formula

a(n+1) = Sum_{k=0..n} A132393(n,k)*5^k*8^(n-k). - Philippe Deléham, Nov 09 2008

a(n) = (-3)^n*Sum_{k=0..n} (8/3)^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

a(n) - (8*n-11)*a(n-1) = 0. - R. J. Mathar, Sep 04 2016

From Benedict W. J. Irwin, Sep 30 2016: (Start)

a(n) = Product_{k=0..n-1} (8*k+5).

a(n) = 8^n*Gamma(5/8 + n)/Gamma(5/8).

E.g.f: 1/(1 - 8*x)^(5/8). (End)

a(n)/n! ~ 8^n/(Gamma(5/8)*n^(3/8)). - Vaclav Kotesovec, Oct 04 2016

Sum_{n>=1} 1/a(n) = 1 + (1/2)*(e/2)^(1/8)*(Gamma(5/8) - Gamma(5/8, 1/8)). - Amiram Eldar, Dec 20 2022

Maple

seq(8^(n-1)*pochhammer(5/8, n-1), n = 1..20); # G. C. Greubel, Dec 03 2019

Mathematica

Table[Product[(8k+5), {k, 0, n-1}], {n, 0, 20}] (* Benedict W. J. Irwin, Sep 30 2016 *)

Prog

(PARI) vector(20, n, prod(j=0, n-2, 8*j+5) ) \\ G. C. Greubel, Dec 03 2019
(Magma) [Round(8^(n-1)*Gamma(n-1 +5/8)/Gamma(5/8)): n in [1..20]]; // G. C. Greubel, Dec 03 2019
(Sage) [8^(n-1)*rising_factorial(5/8, n-1) for n in (1..20)] # G. C. Greubel, Dec 03 2019

Crossrefs

Cf. A048994, A132393.

Sequence in context: A357338 A195886 A079482 * A157097 A349470 A234295

Adjacent sequences: A147622 A147623 A147624 * A147626 A147627 A147628

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

Status

approved