|
| |
|
|
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
|
|
|
|
1, 3, 63, 3465, 363825, 62214075, 15740160975, 5524796502225, 2569030373534625, 1528573072253101875, 1132672646539548489375, 1022803399825212285905625, 1105650475211054481063980625, 1409704355894094463356575296875
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
STATUS
|
approved
|
| |
|
|
