%I #15 Nov 27 2017 11:08:19

%S 0,0,2,6,54,460,3890,42364,512806,6698724,98496252,1585046584,

%T 27568171818,520043947020,10550553510016,228796551051436,

%U 5291441028244966,129967582592816500,3377869204044947060,92652519380506887784,2674716530794339146244

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

%C All terms are even.

%H Alois P. Heinz, <a href="/A262046/b262046.txt">Table of n, a(n) for n = 0..424</a>

%F a(n) ~ n! / (2 * (log(2))^(n+1)). - _Vaclav Kotesovec_, Nov 27 2017

%p g:= proc(n) option remember; `if`(n<2, 1,

%p add(binomial(n, k)*g(k), k=0..n-1))

%p end:

%p b:= proc(n, i) option remember; `if`(n=0, 0, add(

%p `if`(i=j, g(n-j), b(n-j, j))*binomial(n, j), j=1..n))

%p end:

%p a:= n-> b(n, 0):

%p seq(a(n), n=0..25);

%t 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 *)

%Y Cf. A000670, A261983, A262047.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 09 2015