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A320555
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Number of set partitions of [n] such that for each block b the smallest integer interval containing b has at most five elements and for at least one block c the smallest integer interval containing c has exactly five elements.
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3
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15, 64, 201, 585, 1741, 5375, 16355, 48601, 141921, 410425, 1182828, 3398411, 9728692, 27745449, 78861484, 223573925, 632578393, 1786856056, 5039984789, 14197033194, 39945491361, 112282665839, 315352029653, 885048266680, 2482371076351, 6958712870273
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OFFSET
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5,1
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LINKS
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FORMULA
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MAPLE
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b:= proc(n, m, l) option remember; `if`(n=0, 1,
add(b(n-1, max(m, j), [subsop(1=NULL, l)[],
`if`(j<=m, 0, j)]), j={l[], m+1} minus {0}))
end:
A:= (n, k)-> `if`(n=0, 1, `if`(k<2, k, b(n, 0, [0$(k-1)]))):
a:= n-> (k-> A(n, k) -`if`(k=0, 0, A(n, k-1)))(5):
seq(a(n), n=5..50);
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MATHEMATICA
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b[n_, m_, l_List] := b[n, m, l] = If[n == 0, 1, Sum[b[n - 1, Max[m, j], Append[ReplacePart[l, 1 -> Nothing], If[j <= m, 0, j]]], {j, Append[l, m + 1]~Complement~{0}}]];
A[n_, k_] := If[n == 0, 1, If[k < 2, k, b[n, 0, Array[0 &, k - 1]]]];
a[n_] := With[{k = 5}, A[n, k] - If[k == 0, 0, A[n, k - 1]]];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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