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A352069
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Expansion of e.g.f. 1 / (1 + log(1 - 3*x) / 3).
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4
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1, 1, 5, 42, 492, 7374, 134478, 2887128, 71281656, 1988802720, 61860849552, 2121993490176, 79566300371952, 3237181141173264, 142019158472311248, 6682603650677875584, 335698708873243355136, 17930674324049810882688, 1014685181110897126616448, 60641642160287342580586752
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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) = Sum_{k=0..n} Stirling1(n,k) * k! * (-3)^(n-k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * 3^(k-1) * a(n-k).
a(n) ~ n! * 3^(n+1) * exp(3*n) / (exp(3) - 1)^(n+1). - Vaclav Kotesovec, Mar 03 2022
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MATHEMATICA
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nmax = 19; CoefficientList[Series[1/(1 + Log[1 - 3 x]/3), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! (-3)^(n - k), {k, 0, n}], {n, 0, 19}]
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PROG
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(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1+log(1-3*x)/3))) \\ Michel Marcus, Mar 02 2022
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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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