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A327508
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Number of set partitions of [n] where each subset is again partitioned into seven nonempty subsets.
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2
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1, 0, 0, 0, 0, 0, 0, 1, 28, 462, 5880, 63987, 627396, 5715424, 49330996, 408921513, 3292212924, 26136933186, 211891946448, 1910903676319, 21958686224932, 338516695449108, 6257281367040396, 122152192372692405, 2369188918134769500, 44783158458575933110
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OFFSET
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0,9
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LINKS
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FORMULA
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E.g.f.: exp((exp(x)-1)^7/7!).
a(n) = Sum_{k=0..floor(n/7)} (7*k)! * Stirling2(n,7*k)/(7!^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, 7), j=7..n))
end:
seq(a(n), n=0..27);
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PROG
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(PARI) a(n) = sum(k=0, n\7, (7*k)!*stirling(n, 7*k, 2)/(7!^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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