OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..100
Wikipedia, Partition of a set
MAPLE
b:= proc(n, i, t, m) option remember; `if`(n=0, t^(m-i+1),
`if`((i+m)*(m+1-i)/2<n or i>n, 0, `if`(t=0, 0,
t*b(n, i+1, t, m))+ b(n-i, i+1, t+1, m)))
end:
a:= n-> max(seq(b(k, 1, 0, n), k=0..n*(n+1)/2)):
seq(a(n), n=0..26);
# second Maple program:
a:= proc(h) option remember; local b; b:=
proc(n, m) option remember; `if`(n=0, 1,
b(n-1, m)*m + expand(x^(h-n+1)*b(n-1, m+1)))
end: forget(b); max(coeffs(b(h, 0)))
end:
seq(a(n), n=0..26);
MATHEMATICA
Q[1, t_, s_] := t*s;
Q[n_, t_, s_] := Q[n, t, s] = s*D[Q[n-1, t, s], s] + s*t^n*Q[n-1, t, s] // Expand;
P[n_, t_] := Module[{s}, Q[n, t, s] /. s -> 1];
a[n_] := If[n == 0, 1, Module[{t}, CoefficientList[P[n, t], t] // Max]];
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, Oct 03 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Dec 14 2023
STATUS
approved