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A329260
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Expansion of e.g.f. -log(1 - Sum_{k>=0} x^(2^k) / (2^k)!).
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0
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0, 1, 2, 5, 22, 119, 825, 6810, 65766, 725139, 8997795, 124039530, 1881019965, 31117851270, 557686108980, 10763514011250, 222577767068086, 4909509776289707, 115059754193953599, 2855172351859669458, 74786346248906702415, 2062000166613319934190
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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(0) = 0; a(n) = A209229(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * A209229(n-k) * k * a(k).
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MATHEMATICA
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nmax = 21; CoefficientList[Series[-Log[1 - Sum[x^(2^k)/(2^k)!, {k, 0, Floor[Log[2, nmax]] + 1}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Boole[IntegerQ[Log[2, n]]] + Sum[Binomial[n, k] Boole[IntegerQ[Log[2, n - k]]] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 21}]
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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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