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A297926
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Number of set partitions of [2n] in which the size of the first block is n.
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5
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1, 1, 6, 50, 525, 6552, 93786, 1504932, 26640900, 514083570, 10713538550, 239342496120, 5697111804566, 143759365731100, 3829115870472600, 107260549881604200, 3149703964487098665, 96686987797052290440, 3094969650442399156350, 103079905957566679518300
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OFFSET
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0,3
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COMMENTS
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The blocks are ordered with increasing least elements.
a(0) = 1 by convention.
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LINKS
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FORMULA
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a(n) = binomial(2*n-1,n-1) * Bell(n).
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EXAMPLE
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a(1) = 1: 1|2.
a(2) = 6: 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 14|2|3.
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1,
add(b(n-j)*binomial(n-1, j-1), j=1..n))
end:
a:= n-> binomial(2*n-1, n-1)*b(n):
seq(a(n), n=0..25);
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MATHEMATICA
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b[n_] := b[n] = If[n == 0, 1, Sum[b[n-j]*Binomial[n-1, j-1], {j, 1, n}]];
a[n_] := Binomial[2*n-1, n-1] * b[n];
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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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