OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
FORMULA
E.g.f.: exp(x^2/(1-x^2)) (even powers only, see PARI code).
E.g.f.: exp(x^2/(1-x^2)) = 4/(2-(x^2/(1-x^2))*G(0))-1 where G(k) = 1 - x^4/(x^4 + 4*(1-x^2)^2*(2*k+1)*(2*k+3)/G(k+1) ) (continued fraction). - Sergei N. Gladkovskii, Dec 10 2012
a(n) ~ 2^(2*n) * n^(2*n-1/4) * exp(sqrt(4*n)-2*n-1/2). - Vaclav Kotesovec, Feb 25 2014
D-finite with recurrence a(n) -2*(2*n-1)^2*a(n-1) +4*(n-1)*(n-2)*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Feb 01 2022
a(n) = A206703(2n,n). - Alois P. Heinz, Feb 19 2022
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add((i->
b(n-i)*binomial(n-1, i-1)*i!)(2*j), j=1..n/2))
end:
a:= n-> b(2*n):
seq(a(n), n=0..14); # Alois P. Heinz, Feb 01 2022
MATHEMATICA
Table[n!*SeriesCoefficient[E^(x^2/(1-x^2)), {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Feb 25 2014 *)
PROG
(PARI)
x='x+O('x^66); /* (half) that many terms */
v=Vec(serlaplace(exp(x^2/(1-x^2))));
vector(#v\2, n, v[2*n-1])
/* Joerg Arndt, Jul 29 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Nov 02 2003
EXTENSIONS
More terms from Joerg Arndt, Jul 29 2012.
STATUS
approved