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A331689
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E.g.f.: exp(x/(1 - x)) / (1 - 2*x).
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3
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1, 3, 15, 103, 897, 9471, 117703, 1685475, 27361953, 497111707, 10001175231, 220849928223, 5312868439585, 138337555830423, 3876986580776247, 116375171226474331, 3725295913465848513, 126686907674290095795, 4561317309742758852463, 173343622143918424951767
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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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a(n) = Sum_{k=0..n} binomial(n,k)^2 * k! * A000522(n-k).
a(n) = Sum_{k=0..n} binomial(n,k) * k! * 2^k * A000262(n-k).
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MAPLE
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b:= proc(n) b(n):= `if`(n<0, 0, 1+n*b(n-1)) end:
a:= n-> n!*add(binomial(n, k)*b(k)/k!, k=0..n):
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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]!
A000522[0] = 1; A000522[n_] := Floor[Exp[1] n!]; a[n_] := Sum[Binomial[n, k]^2 k! A000522[n - k], {k, 0, n}]; Table[a[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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