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A331797
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E.g.f.: (exp(x) - 1) * exp(exp(x) - 1) / (2 - exp(x)).
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2
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0, 1, 5, 28, 183, 1401, 12466, 127443, 1478581, 19239274, 277797577, 4409962349, 76355817104, 1432117088325, 28925947345561, 625973017346996, 14449435509751843, 354384392492622789, 9202836581079864186, 252260861877820739167, 7278710020682729662089
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Stirling2(n,k) * A007526(k).
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MATHEMATICA
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nmax = 20; CoefficientList[Series[(Exp[x] - 1) Exp[Exp[x] - 1]/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
A007526[n_] := n! Sum[1/k!, {k, 0, n - 1}]; a[n_] := Sum[StirlingS2[n, k] A007526[k], {k, 0, n}]; Table[a[n], {n, 0, 20}]
Table[(1/2) Sum[Binomial[n, k] HurwitzLerchPhi[1/2, -k, 0] BellB[n - k], {k, 1, n}], {n, 0, 20}]
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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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