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A272603
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Number of permutations of [n] whose cycle lengths are factorials.
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5
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1, 1, 2, 4, 10, 26, 196, 1072, 7484, 42940, 261496, 1477136, 15219832, 134828344, 1488515120, 13692017536, 130252442896, 1123580329232, 14639510308384, 173489066401600, 2528654220104096, 31472160333513376, 402634734214583872, 4645625988351336704, 25925035549644280991680
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: exp( sum(n>=1, x^(n!) / n! ) ).
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MAPLE
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a:= proc(n) option remember; local r, f, i;
if n=0 then 1 else r, f, i:= $0..2;
while f<=n do r:= r +a(n-f)*(f-1)!*
binomial(n-1, f-1); f, i:= f*i, i+1
od; r
fi
end:
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MATHEMATICA
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nmax = 4; egf = Exp[Sum[x^n!/n!, {n, 1, nmax}]] + O[x]^(nmax! + 1); CoefficientList[egf, x]*Range[0, nmax!]! (* Jean-François Alcover, Feb 19 2017 *)
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PROG
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(PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(n=1, 10, x^(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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