OFFSET
1,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..213
FORMULA
a(n) = Product_{k=1..n} (2k-3)(4k-5).
a(n) ~ Gamma(1/4) * 2^(3*n - 5/2) * n^(2*n - 7/4) / (sqrt(Pi) * exp(2*n)). - Vaclav Kotesovec, Nov 19 2023
EXAMPLE
E.g.f.: A(x) = x + 3*x^3/3! + 63*x^5/5! + 3465*x^7/7! +...
A(S(x)) = x where S(x) = Sum_{n>=1} A159601(n)*x^(2n-1)/(2n-1)! :
S(x) = x - 3*x^3/3! + 27*x^5/5! - 441*x^7/7! + 11529*x^9/9! +...
MATHEMATICA
Table[Product[(2k-3)(4k-5), {k, n}], {n, 15}] (* Harvey P. Dale, Jan 31 2023 *)
PROG
(PARI) a(n)=prod(k=1, n, (2*k-3)*(4*k-5))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 11 2009
STATUS
approved