A096939 Number of sets of odd number of even lists, cf. A000262.

0, 2, 6, 36, 260, 1950, 19362, 193256, 2326536, 29272410, 413257790, 6231230412, 101415565836, 1769925341366, 32734873484250, 646218442877520, 13404753632014352, 294656673023216946, 6775966692145553526

Offset: 1

Author

Vladeta Jovovic, Aug 18 2004

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000262, A088026, A088009, A096965.

Programs

Mathematica

Drop[ Range[0, 20]! CoefficientList[ Series[ Exp[(x/(1 - x^2))] Sinh[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))*sinh(x^2/(1-x^2)).

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

a(n) = A000262(n) - A096965(n). - Alois P. Heinz, Dec 01 2021

Extensions

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