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A271770
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Number of set partitions of [n] with minimal block length multiplicity equal to ten.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 654729075, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1228555090548911125, 55437426478058625, 1034831960923761000, 375268733082243000, 42378561928787584500, 2126522820799377000, 2014348742002209863250, 10413707343032243250
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OFFSET
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10,11
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LINKS
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FORMULA
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MAPLE
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with(combinat):
b:= proc(n, i, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(multinomial(n, n-i*j, i$j)
*b(n-i*j, i-1, k)/j!, j={0, $k..n/i})))
end:
a:= n-> b(n$2, 10)-b(n$2, 11):
seq(a(n), n=10..40);
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MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[multinomial[n, Join[{n - i*j}, Table[i, j]]]*b[n - i*j, i - 1, k]/j!, {j, Join[{0}, Range[k, n/i]]}]]];
a[n_] := b[n, n, 10] - b[n, n, 11];
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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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