A262047 Number of ordered partitions of [n] such that at least two parts have the same size.

0, 0, 2, 6, 66, 510, 4280, 46536, 542962, 7074654, 101914512, 1621871196, 28087868160, 526841965260, 10641234260358, 230278335503586, 5315641087796562, 130370690653563150, 3385534274596691456, 92801584815121975452, 2677687776095609649256

Offset

0,3

Comments

All terms are even.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..424

Formula

a(n) = A000670(n) - A032011(n).

Maple

g:= proc(n) option remember; `if`(n<2, 1,
       add(binomial(n, k)*g(k), k=0..n-1))
    end:
b:= proc(n, i, p) option remember;
      `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
      `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(n, i))))
    end:
a:= n-> g(n)-b(n$2, 0):
seq(a(n), n=0..25);

Mathematica

g[n_] := g[n] = If[n<2, 1, Sum[Binomial[n, k]*g[k], {k, 0, n-1}]]; b[n_, i_, p_] := b[n, i, p] = If[i*(i+1)/2<n, 0, If[n==0, p!, b[n, i-1, p] + If[i>n, 0, b[n-i, i-1, p+1]*Binomial[n, i]]]]; a[n_] := g[n] - b[n, n, 0]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Crossrefs

Cf. A000670, A032011, A262046, A261982.

Sequence in context: A055685 A368511 A368512 * A280393 A239696 A335645

Adjacent sequences: A262044 A262045 A262046 * A262048 A262049 A262050

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2015

Status

approved