OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..220
FORMULA
E.g.f.: Product_{k>0} cosh(x^k/k).
a(n) ~ c * (2*n-1)! / n ~ c * sqrt(Pi) * n^(2*n-3/2) * 2^(2*n) / exp(2*n), where c = A249673 = Product_{k>=1} cosh(1/k) = 2.1164655365... . - Vaclav Kotesovec, Mar 19 2016
EXAMPLE
a(2)=4 because we have (1)(2)(3)(4), (12)(34), (13)(24) and (14)(23).
MAPLE
g:=product(cosh(x^k/k), k=1..30): gser:=series(g, x=0, 30): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..13); # Emeric Deutsch, Aug 24 2007
# second Maple program:
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(j=0 or irem(j, 2)=0, multinomial(n, n-i*j, i$j)
*(i-1)!^j/j!*b(n-i*j, i-1), 0), j=0..n/i)))
end:
a:= n-> b(2*n$2):
seq(a(n), n=0..20); # Alois P. Heinz, Mar 09 2015
MATHEMATICA
nn=26; Select[Range[0, nn]!CoefficientList[Series[Product[Cosh[x^k/k], {k, 1, nn}], {x, 0, nn}], x], #>0&] (* Geoffrey Critzer, Sep 17 2013 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 06 2007
EXTENSIONS
More terms from Emeric Deutsch, Aug 24 2007
STATUS
approved