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A320760
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Number of ordered set partitions of [n] where the maximal block size equals four.
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2
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1, 10, 120, 1540, 21490, 326970, 5402250, 96500250, 1855334250, 38228190000, 840776937000, 19666511865000, 487617137007000, 12776791730703000, 352825452012033000, 10242418813814187000, 311854958169459705000, 9937942309809373860000, 330821844137019184950000
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OFFSET
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4,2
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LINKS
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FORMULA
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E.g.f.: 1/(1-Sum_{i=1..4} x^i/i!) - 1/(1-Sum_{i=1..3} x^i/i!).
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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))(4):
seq(a(n), n=4..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 = 4}, 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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