OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..370
FORMULA
E.g.f.: B(x) of b(n) where b(2*n)=a(n), b(2*n+1)=0. B(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-2), j=0..min(1, n/i))))
end:
a:= n-> b(2*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 - 2], {j, 0, Min[1, n/i]}]]]; a[n_] := b[2 n, 2 n]; Table[ a[n], {n, 0, 30}] (* Jean-François Alcover, Jan 22 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 18 2006
STATUS
approved