OFFSET
1,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..500
FORMULA
E.g.f.: sinh(exp(x)-x-1).
EXAMPLE
a(6)=16 since we can partition a set of six labeled elements into one non-singleton block in 1 way and into three non-singleton blocks (each necessarily of size 2) in 15 ways; thus a(6) = 1+15 = 16.
MAPLE
seq(coeff(series(sinh(exp(x)-x-1), x=0, 25), x^i)*i!, i=1..24);
# second Maple program:
with(combinat):
b:= proc(n, i, t) option remember; `if`(n=0, t,
`if`(i<2, 0, add(multinomial(n, n-i*j, i$j)/j!*
b(n-i*j, i-1, irem(t+j, 2)), j=0..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=1..30); # Alois P. Heinz, Mar 08 2015
MATHEMATICA
multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_, t_] := b[n, i, t] = If[n == 0, t, If[i < 2, 0, Sum[multinomial[n, Join[{n - i*j}, Array[i&, j]]]/j!*b[n - i*j, i - 1, Mod[t + j, 2]], {j, 0, n/i}]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jan 10 2016, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Isabel C. Lugo (izzycat(AT)gmail.com), Aug 23 2004
STATUS
approved