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A324241
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Number of set partitions of [2n] where each subset is again partitioned into n nonempty subsets.
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2
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1, 2, 10, 100, 1736, 42651, 1324114, 49330996, 2141770488, 106175420065, 5917585057033, 366282501223002, 24930204592110338, 1850568574258750360, 148782988064395367700, 12879868072770703598760, 1194461517469808134322280, 118144018577011379763287565
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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a(2) = 10: 123/4, 124/3, 12/34, 134/2, 13/24, 14/23, 1/234, 1/2|3/4, 1/3|2/4, 1/4|2/3.
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MAPLE
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b:= proc(n, k) option remember; `if`(n=0, 1, add(b(n-j, k)
*binomial(n-1, j-1)*Stirling2(j, k), j=k..n))
end:
a:= n-> b(2*n, n):
seq(a(n), n=0..18);
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MATHEMATICA
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b[n_, k_] := b[n, k] = If[n == 0, 1, If[k == 0 || k > n, 0, Sum[b[n-j, k]* Binomial[n - 1, j - 1] StirlingS2[j, k], {j, k, n}]]];
a[n_] := b[2n, n];
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PROG
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(PARI) a(n) = if(n==0, 1, stirling(2*n, n, 2)+binomial(2*n, n)/2); \\ Seiichi Manyama, May 08 2022
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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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