OFFSET
1,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..500
FORMULA
Exponential generating function: cosh(exp(x)-x-1).
EXAMPLE
a(6)=25 since we can partition a set of six elements into two non-singleton blocks, either of sizes four and two (15 ways) or three and three (10 ways); a(6)=15+10=25.
MAPLE
seq(coeff(series(cosh(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, 1):
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, 1]; 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