OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..445
FORMULA
E.g.f.: exp(x/(1-x^2))*Product_{k>0} cosh(x^(2*k)).
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(i::even and j::odd, 0, b(n-i*j, i-1)*
multinomial(n, n-i*j, i$j)/j!*i!^j), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..25); # Alois P. Heinz, May 10 2016
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[If[EvenQ[i] && OddQ[j], 0, b[n-i*j, i- 1] * multinomial[n, Join[{n - i*j}, Array[i &, j]]]/j!*i!^j], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 05 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Feb 10 2005
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, May 10 2016
STATUS
approved