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

%I A262047 #10 Feb 15 2017 11:14:52
%S A262047 0,0,2,6,66,510,4280,46536,542962,7074654,101914512,1621871196,
%T A262047 28087868160,526841965260,10641234260358,230278335503586,
%U A262047 5315641087796562,130370690653563150,3385534274596691456,92801584815121975452,2677687776095609649256
%N A262047 Number of ordered partitions of [n] such that at least two parts have the same size.
%C A262047 All terms are even.
%H A262047 Alois P. Heinz, <a href="/A262047/b262047.txt">Table of n, a(n) for n = 0..424</a>
%F A262047 a(n) = A000670(n) - A032011(n).
%p A262047 g:= proc(n) option remember; `if`(n<2, 1,
%p A262047        add(binomial(n, k)*g(k), k=0..n-1))
%p A262047     end:
%p A262047 b:= proc(n, i, p) option remember;
%p A262047       `if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p)+
%p A262047       `if`(i>n, 0, b(n-i, i-1, p+1)*binomial(n, i))))
%p A262047     end:
%p A262047 a:= n-> g(n)-b(n$2, 0):
%p A262047 seq(a(n), n=0..25);
%t A262047 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 *)
%Y A262047 Cf. A000670, A032011, A262046, A261982.
%K A262047 nonn
%O A262047 0,3
%A A262047 _Alois P. Heinz_, Sep 09 2015