OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1 - 8*x)^(-5/4).
a(n) ~ 4*Gamma(1/4)^-1*n^(1/4)*2^(3*n)*{1 + 5/32*n^-1 - ...}
a(n) = 8^n*binomial(1/4 + n, 1/4).
E.g.f.: is the hypergeometric function of type 1F1, in Maple notation hypergeom([5/4], [1], 8*x). - Karol A. Penson, Dec 20 2015
D-finite with recurrence: n*a(n) +2*(-4*n-1)*a(n-1)=0. - R. J. Mathar, Jan 16 2020
MAPLE
a:= n-> (2^n/n!)*mul(4*k+5, k=0..n-1); seq(a(n), n=0..25); # G. C. Greubel, Aug 22 2019
MATHEMATICA
Table[2^n/n! Product[4k+5, {k, 0, n-1}], {n, 0, 25}] (* Harvey P. Dale, Apr 15 2019 *)
Table[8^n*Pochhammer[5/4, n]/n!, {n, 0, 25}] (* G. C. Greubel, Aug 22 2019 *)
PROG
(PARI) a(n)=2^n/n!*prod(k=0, n-1, 4*k+5)
for(n=0, 21, print(a(n)))
(Magma) [1] cat [2^n*&*[4*k+5: k in [0..n-1]]/Factorial(n): n in [1..25]]; // G. C. Greubel, Aug 22 2019
(Sage) [8^n*rising_factorial(5/4, n)/factorial(n) for n in (0..25)] # G. C. Greubel, Aug 22 2019
(GAP) List([0..25], n-> 2^n*Product([0..n-1], k-> 4*k+5)/Factorial(n) ); # G. C. Greubel, Aug 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joe Keane (jgk(AT)jgk.org)
EXTENSIONS
More terms from Rick L. Shepherd, Mar 03 2002
Terms a(20) onward added by G. C. Greubel, Aug 22 2019
STATUS
approved