A262046 Number of ordered partitions of [n] such that at least two adjacent parts have the same size.

0, 0, 2, 6, 54, 460, 3890, 42364, 512806, 6698724, 98496252, 1585046584, 27568171818, 520043947020, 10550553510016, 228796551051436, 5291441028244966, 129967582592816500, 3377869204044947060, 92652519380506887784, 2674716530794339146244

Offset

0,3

Comments

All terms are even.

Links

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

Formula

a(n) ~ n! / (2 * (log(2))^(n+1)). - Vaclav Kotesovec, Nov 27 2017

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) option remember; `if`(n=0, 0, add(
      `if`(i=j, g(n-j), b(n-j, j))*binomial(n, j), j=1..n))
    end:
a:= n-> b(n, 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_] := b[n, i] = If[n==0, 0, Sum[If[i==j, g[n-j], b[n-j, j]]*Binomial[n, j], {j, 1, n}]]; a[n_] := b[n, 0]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Crossrefs

Cf. A000670, A261983, A262047.

Sequence in context: A337510 A259553 A327425 * A280982 A219692 A085078

Adjacent sequences: A262043 A262044 A262045 * A262047 A262048 A262049

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2015

Status

approved