A159605 E.g.f: Sum_{n>=1} a(n)*x^(2n-1)/(2n-1)! = Series_Reversion of e.g.f. S(x) of A159601.

1, 3, 63, 3465, 363825, 62214075, 15740160975, 5524796502225, 2569030373534625, 1528573072253101875, 1132672646539548489375, 1022803399825212285905625, 1105650475211054481063980625, 1409704355894094463356575296875

Offset: 1

Author

Paul D. Hanna, May 11 2009

Keywords

• nonn

Examples

			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! +...
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..213

Crossrefs

Cf. A159601.

Programs

Mathematica

Table[Product[(2k-3)(4k-5),{k,n}],{n,15}] (* Harvey P. Dale, Jan 31 2023 *)

PARI

a(n)=prod(k=1,n,(2*k-3)*(4*k-5))

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