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A212599
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Number of functions on n labeled points to themselves (endofunctions) such that the number of cycles of f that have each even size is even.
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3
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1, 1, 3, 18, 160, 1875, 27126, 466186, 9275064, 209654325, 5307031000, 148720701426, 4570816040352, 152874605142727, 5527634477245440, 214862754390554250, 8934811701563214976, 395788795274021394729, 18606559519007667893376, 925222631836457779380370, 48518852386696450625510400
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..200
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FORMULA
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E.g.f.: ((1+T(x))/(1-T(x)))^(1/2) * Product_{i>=1} cosh(T(x)^(2*i)/(2*i)) where T(x) is the e.g.f. for A000169.
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MAPLE
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with(combinat):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(irem(j, igcd(i, 2))<>0, 0, (i-1)!^j*
multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1)), j=0..n/i)))
end:
a:= n-> add(b(j, j)*n^(n-j)*binomial(n-1, j-1), j=0..n):
seq(a(n), n=0..25); # Alois P. Heinz, Sep 08 2014
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MATHEMATICA
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nn=20; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; p=Product[Cosh[t^(2i)/(2i)], {i, 1, nn}]; Range[0, nn]! CoefficientList[Series[((1+t)/(1-t))^(1/2) p, {x, 0, nn}], x]
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CROSSREFS
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Cf. A003483, A246951, A116956.
Sequence in context: A089901 A238302 A067302 * A052182 A301371 A115415
Adjacent sequences: A212596 A212597 A212598 * A212600 A212601 A212602
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KEYWORD
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nonn,nice
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AUTHOR
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Geoffrey Critzer, May 22 2012
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EXTENSIONS
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Maple program fixed by Vaclav Kotesovec, Sep 13 2014
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STATUS
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approved
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