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

1,2

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

Cf. A159601.

Sequence in context: A331012 A369955 A123687 * A180761 A156904 A193100

Adjacent sequences: A159602 A159603 A159604 * A159606 A159607 A159608

Keyword

nonn

Author

Paul D. Hanna, May 11 2009

Status

approved