OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
E.g.f.: exp(sinh(x)) * Product {m >= 1} (1+x^(2*m)/(2*m)!).
MAPLE
with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), j=0..min(
`if`(irem(i, 2)=0, 1, n), n/i))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30); # Alois P. Heinz, Mar 08 2015
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j! * b[n-i*j, i-1], {j, 0, Min[If[Mod[i, 2]==0, 1, n], n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 25 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 18 2006
STATUS
approved