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A184975
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E.g.f. exp((1-sqrt(1-4*log(1+x)))/2).
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1
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1, 1, 2, 12, 106, 1330, 21188, 412496, 9471180, 250752012, 7519114872, 251898595344, 9324409750104, 377947150828728, 16648683024776112, 791945577071452608, 40457530872588060816, 2209174906291706917008, 128405210614917271843872, 7915238091104410779024576
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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=1..n} (Sum_{i=0..(n-k)} ((i+k-1)!*C(k+2*i-1,i+k-1) *stirling1(n, i+k))))/(k-1)!), n>0, a(0)=1.
a(n) ~ n^(n-1) / (sqrt(2)*exp(n-3/8)*(exp(1/4)-1)^(n-1/2)). - Vaclav Kotesovec, Jun 02 2013
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MATHEMATICA
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CoefficientList[Series[Exp[(1-Sqrt[1-4*Log[1+x]])/2], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 02 2013 *)
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PROG
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(Maxima) a(n):=if n=0 then 1 else sum((sum(((i+k-1)!*binomial(k+2*i-1, i+k-1) *stirling1(n, i+k)), i, 0, n-k))/(k-1)!, k, 1, n);
(PARI) x='x+O('x^50); Vec(serlaplace(exp((1-sqrt(1-4*log(1+x)))/2))) \\ G. C. Greubel, Jun 02 2017
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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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