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A262046
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Number of ordered partitions of [n] such that at least two adjacent parts have the same size.
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15
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0, 0, 2, 6, 54, 460, 3890, 42364, 512806, 6698724, 98496252, 1585046584, 27568171818, 520043947020, 10550553510016, 228796551051436, 5291441028244966, 129967582592816500, 3377869204044947060, 92652519380506887784, 2674716530794339146244
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OFFSET
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0,3
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COMMENTS
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All terms are even.
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LINKS
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FORMULA
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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