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A242676
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a(n) = Abs(StirlingS1(4*n,n)).
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2
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1, 6, 13068, 150917976, 5056995703824, 371384787345228000, 50779532534302850198976, 11616723683566425573507775872, 4123257155075936045020928754053376, 2146734309994687055429549444238169536000, 1569808063009967047226374755685187772671339520
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OFFSET
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0,2
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COMMENTS
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Generally, for p>=2 is Abs(StirlingS1(p*n,n)) asymptotic to n^((p-1)*n) * c^(p*n) * p^((2*p-1)*n) / (sqrt(2*Pi*p*(c-1)*n) * exp((p-1)*n) * (c*p-1)^((p-1)*n)), where c = -LambertW(-1,-exp(-1/p)/p).
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LINKS
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FORMULA
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a(n) ~ n^(3*n) * c^(4*n) * 2^(14*n-1) / (sqrt(2*Pi*(c-1)*n) * exp(3*n) * (4*c-1)^(3*n)), where c = -LambertW(-1,-exp(-1/4)/4) = 2.58666298226305388118285...
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MAPLE
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seq(abs(Stirling1(4*n, n)), n=0..20);
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MATHEMATICA
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Table[Abs[StirlingS1[4*n, n]], {n, 0, 20}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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