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A335981
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Expansion of e.g.f. exp(3 * (1 - exp(-x)) + x).
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3
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1, 4, 13, 31, 40, -23, -95, 490, 823, -8393, 3766, 174775, -658787, -2751404, 34033297, -55552037, -1170734432, 9362348365, 3277050925, -562286419646, 3848880970147, 8815342530739, -356804325202730, 2389771436686339, 8677476137729929, -302470260552857660
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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) = exp(3) * (-1)^n * Sum_{k>=0} (-3)^k * (k - 1)^n / k!.
a(0) = 1; a(n) = a(n-1) + 3 * Sum_{k=0..n-1} (-1)^(n-k-1) * binomial(n-1,k) * a(k).
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MATHEMATICA
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nmax = 25; CoefficientList[Series[Exp[3 (1 - Exp[-x]) + x], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = a[n - 1] + 3 Sum[(-1)^(n - k - 1) Binomial[n - 1, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 25}]
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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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