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A147625 Octo-factorial numbers(4). 5
1, 5, 65, 1365, 39585, 1464645, 65909025, 3493178325, 213083877825, 14702787569925, 1132114642884225, 96229744645159125, 8949366251999798625, 903885991451979661125, 98523573068265783062625 (list; graph; refs; listen; history; text; internal format)
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

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: A056245 A195886 A079482 * A157097 A234295 A251575

Adjacent sequences:  A147622 A147623 A147624 * A147626 A147627 A147628

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Nov 08 2008

STATUS

approved

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Last modified June 24 06:17 EDT 2021. Contains 345416 sequences. (Running on oeis4.)