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A245959
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Number of endofunctions f on [2n] satisfying f^3(i) = i for all i in [n].
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3
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1, 2, 36, 1440, 84624, 7675200, 962250624, 151851992544, 30421572307200, 7430515709340672, 2142144445293849600, 727442024443449689088, 285148327160858698469376, 127152465871110917459189760, 64226006581334387301393186816, 36322574197169989225245335040000
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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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MAPLE
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with(combinat): M:=multinomial:
T:= proc(n, k) local l, g; l, g:= [1, 3],
proc(k, m, i, t) option remember; local d, j; d:= l[i];
`if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*
(d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,
`if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),
`if`(t=0, [][], m/t))))
end; g(k, n-k, nops(l), 0)
end:
a:= n-> T(2*n, n):
seq(a(n), n=0..20);
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MATHEMATICA
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M[n_, m_, k_List] := n!/Times @@ (Join[{m}, k]!);
T[0, 0] = 1; T[n_, k_] := T[n, k] = Module[{l = {1, 3}, g}, g[k0_, m_, {i_, t_}] := g[k0, m, i, t]; g[k0_, m_, i_, t_] := g[k0, m, i, t] = Module[ {d}, d = l[[i]]; If[i == 1, n^m, Sum[M[k0, k0 - (d - t)*j, Table[(d - t), {j}]]/j!*(d - 1)!^j*M[m, m - t*j, Table[t, {j}]]*g[k0 - (d - t)*j, m - t*j, If[d - t == 1, {i - 1, 0}, {i, t + 1}]], {j, 0, Min[k0/(d - t), If[t == 0, Infinity, m/t]]}]]]; g[k, n - k, Length[l], 0]];
a[n_] := T[2 n, n];
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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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