OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1 - 8*x)^(-7/4).
a(n) ~ 4/3*Gamma(3/4)^-1*n^(3/4)*2^(3*n)*{1 + 21/32*n^-1 - ...}.
D-finite with recurrence: n*a(n) +2*(-4*n-3)*a(n-1)=0. - R. J. Mathar, Jan 17 2020
MAPLE
seq(2^n/n!*mul(4*k + 7, k=0..n-1), n=0..30);
MATHEMATICA
Table[2^n/n! Product[4k+7, {k, 0, n-1}], {n, 0, 25}] (* Harvey P. Dale, Apr 26 2019 *)
Table[8^n*Pochhammer[7/4, n]/n!, {n, 0, 25}] (* G. C. Greubel, Aug 22 2019 *)
PROG
(PARI) a(n) = 2^n*prod(k=0, n-1, 4*k+7)/n!;
vector(25, n, n--; a(n)) \\ G. C. Greubel, Aug 22 2019
(Magma) [1] cat [2^n*(&*[4*k+7: k in [0..n-1]])/Factorial(n): n in [1..25]]; // G. C. Greubel, Aug 22 2019
(Sage) [8^n*rising_factorial(7/4, 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+7)/Factorial(n) ); # G. C. Greubel, Aug 22 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Joe Keane (jgk(AT)jgk.org)
EXTENSIONS
More terms from Sascha Kurz, Mar 24 2002
STATUS
approved