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A320758
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Number of ordered set partitions of [n] where the maximal block size equals two.
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2
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1, 6, 42, 330, 2970, 30240, 345240, 4377240, 61122600, 933055200, 15470254800, 277005128400, 5329454130000, 109681187616000, 2404894892400000, 55977698400624000, 1378748676601296000, 35829233832135744000, 979763376201049440000, 28124715476056399200000
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OFFSET
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2,2
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LINKS
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FORMULA
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E.g.f.: 1/(1-Sum_{i=1..2} x^i/i!) - 1/(1-x).
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MAPLE
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b:= proc(n, k) option remember; `if`(n=0, 1, add(
b(n-i, k)*binomial(n, i), i=1..min(n, k)))
end:
a:= n-> (k-> b(n, k) -b(n, k-1))(2):
seq(a(n), n=2..25);
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];
a[n_] := With[{k = 2}, b[n, k] - b[n, k-1]];
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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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