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) = |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