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A328155
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Number of set partitions of [n] with distinct block sizes and one of the block sizes is 3.
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3
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0, 0, 0, 1, 4, 10, 60, 35, 336, 1848, 16080, 33825, 93280, 539396, 3856216, 49390250, 147478800, 708041160, 2354289744, 18196716309, 150847235040, 2615953578700, 9488756856040, 57565330671310, 296745669669768, 1435526275752900, 12231628020365000
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OFFSET
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0,5
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LINKS
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MAPLE
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b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, 1, `if`(i<2, 0, b(n, i-1, `if`(i=k, 0, k)))+
`if`(i=k, 0, b(n-i, min(n-i, i-1), k)*binomial(n, i))))
end:
a:= n-> b(n$2, 0)-b(n$2, 3):
seq(a(n), n=0..29);
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MATHEMATICA
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b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n == 0, 1, If[i < 2, 0, b[n, i - 1, If[i == k, 0, k]]] + If[i == k, 0, b[n - i, Min[n - i, i - 1], k]*Binomial[n, i]]]];
a[n_] := b[n, n, 0] - b[n, n, 3];
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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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