A096965 Number of sets of even number of even lists, cf. A000262.

1, 1, 1, 7, 37, 241, 2101, 18271, 201097, 2270017, 29668681, 410815351, 6238931821, 101560835377, 1765092183037, 32838929702671, 644215775792401, 13441862819232001, 293976795292186897, 6788407001443004647, 163735077313046119861, 4142654439686285737201

Offset: 0

Author

Vladeta Jovovic, Aug 18 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000262, A088026, A088009, A096939, A349776.

Programs

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 *)

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)

Extensions

More terms from Robert G. Wilson v, Aug 19 2004

a(0)=1 prepended by Alois P. Heinz, Dec 01 2021