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A336959
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E.g.f.: 1 / (1 - x * exp(-2*x)).
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2
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1, 1, -2, -6, 40, 120, -1872, -3920, 155776, 56448, -19946240, 44799744, 3588719616, -21265587200, -850126505984, 9423227873280, 251457224998912, -4665150579572736, -88212028284665856, 2663461772025462784, 34353949630376181760, -1756678038088484388864
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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) = n! * Sum_{k=0..n} (-2 * (n-k))^k / k!.
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k * (-2)^(k-1) * a(n-k).
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MATHEMATICA
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nmax = 21; CoefficientList[Series[1/(1 - x Exp[-2 x]), {x, 0, nmax}], x] Range[0, nmax]!
Join[{1}, Table[n! Sum[(-2 (n - k))^k/k!, {k, 0, n}], {n, 1, 21}]]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k (-2)^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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