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A352071
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Expansion of e.g.f. 1 / (1 + log(1 - 4*x) / 4).
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4
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1, 1, 6, 62, 904, 16984, 390128, 10586736, 331267200, 11738697600, 464539452672, 20302660659456, 971106358760448, 50452643588275200, 2829000818124208128, 170271405502300207104, 10948525752699316371456, 748994717201835804033024, 54315931193865932254543872
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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! * (-4)^(n-k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * 4^(k-1) * a(n-k).
a(n) ~ n! * 4^(n+1) * exp(4*n) / (exp(4) - 1)^(n+1). - Vaclav Kotesovec, Mar 03 2022
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MATHEMATICA
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nmax = 18; CoefficientList[Series[1/(1 + Log[1 - 4 x]/4), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] k! (-4)^(n - k), {k, 0, n}], {n, 0, 18}]
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PROG
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(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1+log(1-4*x)/4))) \\ 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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