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
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Nov 08 2008
STATUS
approved