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A327509
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Number of set partitions of [n] where each subset is again partitioned into eight nonempty subsets.
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2
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1, 0, 0, 0, 0, 0, 0, 0, 1, 36, 750, 11880, 159027, 1899612, 20912320, 216627840, 2141770488, 20416870188, 189100389270, 1713143123640, 15314761051669, 137723007972924, 1310008783707360, 14647748873844240, 215375952901752225, 4079250159907459680
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OFFSET
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0,10
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LINKS
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FORMULA
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E.g.f.: exp((exp(x)-1)^8/8!).
a(n) = Sum_{k=0..floor(n/8)} (8*k)! * Stirling2(n,8*k)/(8!^k * k!). - Seiichi Manyama, May 07 2022
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)
*binomial(n-1, j-1)*Stirling2(j, 8), j=8..n))
end:
seq(a(n), n=0..27);
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PROG
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(PARI) a(n) = sum(k=0, n\8, (8*k)!*stirling(n, 8*k, 2)/(8!^k*k!)); \\ Seiichi Manyama, May 07 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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