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A331688
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E.g.f.: exp(-x/(1 - x)) / (1 - 2*x).
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2
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1, 1, 3, 17, 137, 1389, 16819, 236557, 3792753, 68326073, 1366917731, 30074632521, 721798881913, 18766625660197, 525460685327187, 15763716503597189, 504436925448024929, 17150818356045629937, 617428780939911647683, 23462281235407345160833
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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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a(n) = Sum_{k=0..n} binomial(n,k)^2 * k! * A000166(n-k).
a(n) = Sum_{k=0..n} binomial(n,k) * k! * 2^k * A293116(n-k).
a(n) = (4*n-3)*a(n-1)-(n-1)*(5*n-8)*a(n-2)+2*(n-1)*(n--2)^2*a(n-3). - Robert Israel, Jul 28 2020
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MAPLE
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f:= gfun:-rectoproc({a(n) = -(n - 1)*(5*n - 8)*a(n - 2) + (-3 + 4*n)*a(n - 1) + 2*(n - 1)*(n - 2)^2*a(n - 3), a(0)=1, a(1)=1, a(2)=3}, a(n), remember):
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MATHEMATICA
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nmax = 19; CoefficientList[Series[Exp[-x/(1 - x)]/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k]^2 k! Subfactorial[n - k], {k, 0, n}], {n, 0, 19}]
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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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