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A346427
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E.g.f.: -log(1 - log(1 + x) * exp(x)).
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1
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0, 1, 2, 7, 29, 183, 1319, 12122, 124802, 1508581, 20150509, 302637564, 4960500764, 89164162579, 1730245993111, 36241995276276, 812108432244304, 19430625834864633, 493622198791114665, 13283773364613034324, 377224137563670860492, 11278211794764786428831
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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) = -(-1)^n * A002741(n) - (1/n) * Sum_{k=1..n-1} (-1)^(n-k) * binomial(n,k) * A002741(n-k) * k * a(k).
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MATHEMATICA
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nmax = 21; CoefficientList[Series[-Log[1 - Log[1 + x] Exp[x]], {x, 0, nmax}], x] Range[0, nmax]!
A002741[n_] := A002741[n] = n! Sum[(-1)^k/((n - k) k!), {k, 0, n - 1}]; a[0] = 0; a[n_] := a[n] = -(-1)^n A002741[n] - (1/n) Sum[(-1)^(n - k) Binomial[n, k] A002741[n - k] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 21}]
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PROG
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(PARI) my(x='x+O('x^25)); concat(0, Vec(serlaplace(-log(1 - log(1+x) * exp(x))))) \\ Michel Marcus, Jul 19 2021
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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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