OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..500
FORMULA
E.g.f.: exp(sinh(x))*Product_{k>0} (1+sinh(x^(2*k)/(2*k)!)).
EXAMPLE
a(4)=12 because from the 15 (=A000110(4)) partitions of the 4-set {a,b,c,d} only the partitions ab|cd, ac|bd and ad|bc do not qualify.
MAPLE
g:=exp(sinh(x))*(product(1+sinh(x^(2*k)/factorial(2*k)), k=1..25)): gser:= series(g, x=0, 30): seq(factorial(n)*coeff(gser, x, n), n=0..23); # Emeric Deutsch, Aug 28 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, 2)=1 or irem(j, 2)=1, multinomial(
n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..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[If[j == 0 || Mod[i, 2] == 1 || Mod[j, 2] == 1, multinomial[n, Join[{ n - i*j}, Array[i &, j]]]/j!*b[n - i*j, i - 1], 0], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 22 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 05 2007, Aug 05 2007
EXTENSIONS
More terms from Emeric Deutsch, Aug 28 2007
STATUS
approved