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A096965
Number of sets of even number of even lists, cf. A000262.
3
1, 1, 1, 7, 37, 241, 2101, 18271, 201097, 2270017, 29668681, 410815351, 6238931821, 101560835377, 1765092183037, 32838929702671, 644215775792401, 13441862819232001, 293976795292186897, 6788407001443004647, 163735077313046119861, 4142654439686285737201
OFFSET
0,4
LINKS
FORMULA
E.g.f.: exp(x/(1-x^2))*cosh(x^2/(1-x^2)).
a(n) = (n!*sum(m=floor((n+1)/2)..n, (binomial(n-1,2*m-n-1))/(2*m-n)!)). - Vladimir Kruchinin, Mar 10 2013
Recurrence: (n-2)*a(n) = (2*n-3)*a(n-1) + (n-1)*(2*n^2 - 8*n + 7)*a(n-2) + (n-2)*(n-1)*(2*n-5)*a(n-3) - (n-4)*(n-3)*(n-2)^2*(n-1)*a(n-4). - Vaclav Kotesovec, Sep 29 2013
a(n) ~ exp(2*sqrt(n)-n-1/2)*n^(n-1/4)/(2*sqrt(2)) * (1-5/(48*sqrt(n))). - Vaclav Kotesovec, Sep 29 2013
From Alois P. Heinz, Dec 01 2021: (Start)
a(n) = A000262(n) - A096939(n).
a(n) = |Sum_{k=0..n} (-1)^k * A349776(n,k)|. (End)
MAPLE
a:= proc(n) option remember; `if`(n<4, [1$3, 7][n+1], ((2*n-3)
*a(n-1)+(n-1)*(2*n^2-8*n+7)*a(n-2) + (n-2)*(n-1)*(2*n-5)
*a(n-3)-(n-4)*(n-3)*(n-2)^2*(n-1)*a(n-4))/(n-2))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Dec 01 2021
MATHEMATICA
Drop[ Range[0, 20]! CoefficientList[ Series[ Exp[(x/(1 - x^2))]Cosh[x^2/(1 - x^2)], {x, 0, 20}], x], 1] (* Robert G. Wilson v, Aug 19 2004 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 18 2004
EXTENSIONS
More terms from Robert G. Wilson v, Aug 19 2004
a(0)=1 prepended by Alois P. Heinz, Dec 01 2021
STATUS
approved