OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..220
FORMULA
E.g.f.: Product(1+sinh(x^(2*k)/(2*k)),k=1..infinity)*Product(cosh(x^(2*k-1)/(2*k-1)),k=1..infinity).
a(n) ~ c * 4^n * n! * (n-1)!, where c = 0.474431... - Vaclav Kotesovec, Jul 21 2019
EXAMPLE
a(2)=13 because we have (1)(2)(3)(4), six permutations of type (p)(q)(rs) and six permutations of type (pqrs).
MAPLE
g:=product((1+sinh(x^(2*k)/(2*k)))*cosh(x^(2*k-1)/(2*k-1)), k=1..25): gser:= series(g, x=0, 30): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..13); # Emeric Deutsch, Sep 04 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(i+j, 2)=1, 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
multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[If[j == 0 || Mod[i + j, 2] == 1, multinomial[n, {n - i j} ~Join~ Table[i, {j}]] (i - 1)!^j/j! b[n - i j, i - 1], 0], {j, 0, n/i}]]];
a[n_] := b[2n, 2n];
a /@ Range[0, 20] (* Jean-François Alcover, Nov 19 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 25 2007
EXTENSIONS
More terms from Emeric Deutsch, Sep 04 2007
STATUS
approved