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

0,4

Links

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

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

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

Sequence in context: A102760 A332906 A361279 * A159597 A217723 A100309

Adjacent sequences: A096962 A096963 A096964 * A096966 A096967 A096968

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