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A088026
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Number of "sets of even lists" for even n, cf. A000262.
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6
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1, 2, 36, 1560, 122640, 15150240, 2695049280, 650948538240, 204637027795200, 81098021561356800, 39516616693678924800, 23204736106751520921600, 16152539421202464036556800, 13145716394493318293898240000, 12363004898960780220305909760000
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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Table[n!*SeriesCoefficient[E^(x^2/(1-x^2)), {x, 0, n}], {n, 0, 40, 2}] (* Vaclav Kotesovec, Feb 25 2014 *)
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PROG
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(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 */
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CROSSREFS
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Cf. A052845, A088009, A206703.
Sequence in context: A245959 A174580 A209803 * A174881 A126934 A303503
Adjacent sequences: A088023 A088024 A088025 * A088027 A088028 A088029
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic, Nov 02 2003
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EXTENSIONS
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More terms from Joerg Arndt, Jul 29 2012.
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STATUS
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approved
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