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A262047
Number of ordered partitions of [n] such that at least two parts have the same size.
3
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 09 2015
STATUS
approved