OFFSET
0,2
LINKS
Clark Kimberling, Table of n, a(n) for n = 0..100
FORMULA
From Derek Orr, Oct 21 2014: (Start)
a(2*n) = (2*n+3)*(2*n+1)!!/3, for n > 0.
a(2*n+1) = (n+2)!*2^(n+1), for n > 0.
For n > 2, if n is even, a(n)/[(n+1)*(n-1)*(n-3)*...*7*5] = n + 3 and if n is odd, a(n)/[(n+1)*(n-1)*(n-3)*...*6*4] = n + 3. (End)
a(n) = gcd_2((n+3)!,(n+3)!!), where gcd_2(b,c) denotes the second-largest common divisor of non-coprime integers b and c, as defined in A309491. - Lechoslaw Ratajczak, Apr 15 2021
D-finite with recurrence: a(n) - (3+n)*a(n-2) = 0. - Georg Fischer, Nov 25 2022
Sum_{n>=0} 1/a(n) = 3*sqrt(e*Pi/2)*erf(1/sqrt(2)) + 2*sqrt(e) - 6, where erf is the error function. - Amiram Eldar, Dec 10 2022
EXAMPLE
MATHEMATICA
PROG
(PARI) f(n) = if (n, x + (n + 3)/f(n-1), 1);
a(n) = polcoef(numerator(f(n)), 0); \\ Michel Marcus, Nov 25 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 20 2014
STATUS
approved