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A032012
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Number of ways to partition n labeled elements into sets of different odd sizes and order the sets.
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1
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1, 1, 0, 1, 8, 1, 12, 1, 128, 3025, 260, 7921, 2048, 78937, 4760, 2375101, 138411008, 9837697, 588189972, 96605425, 7353141248, 1752111145, 151280741480, 9294316285, 12191175684608, 1413604888888801, 75955683963432, 9022098736088101, 1170150933402368
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OFFSET
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0,5
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LINKS
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FORMULA
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"AGJ" (ordered, elements, labeled) transform of 1, 0, 1, 0, ...(odds).
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MAPLE
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b:= proc(n, i, p) option remember;
`if`(n=0, p!, `if`(i<1, 0, b(n, i-2, p)+
`if`(i>n, 0, b(n-i, i-2, p+1)*binomial(n, i))))
end:
a:= n-> b(n, n-1+irem(n, 2), 0):
seq(a(n), n=0..30);
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MATHEMATICA
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b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, b[n, i-2, p] + If[i>n, 0, b[n-i, i-2, p+1]*Binomial[n, i]]]]; a[n_] := b[n, n-1+Mod[n, 2], 0]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 27 2017, translated from Maple *)
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PROG
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(PARI) seq(n)=[subst(serlaplace(y^0*p), y, 1) | p <- Vec(serlaplace(prod(k=1, ceil(n/2), 1 + x^(2*k-1)*y/(2*k-1)! + O(x*x^n))))] \\ Andrew Howroyd, Sep 13 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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