A088026 Number of "sets of even lists" for even n, cf. A000262.

1, 2, 36, 1560, 122640, 15150240, 2695049280, 650948538240, 204637027795200, 81098021561356800, 39516616693678924800, 23204736106751520921600, 16152539421202464036556800, 13145716394493318293898240000, 12363004898960780220305909760000

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

Cf. A052845, A088009, A206703.

Sequence in context: A245959 A174580 A209803 * A174881 A126934 A303503

Adjacent sequences: A088023 A088024 A088025 * A088027 A088028 A088029

Keyword

nonn

Author

Vladeta Jovovic, Nov 02 2003

Extensions

More terms from Joerg Arndt, Jul 29 2012.

Status

approved