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A091695
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Expansion of e.g.f. exp(x/(1-x)^3).
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8
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1, 1, 7, 55, 529, 6121, 82711, 1273567, 21945505, 417540529, 8680953511, 195582295591, 4742407056817, 123045795823705, 3399348471640759, 99573135106176271, 3081061456572152641, 100382623544966098657, 3433727597233037475655, 123000248740384210119319, 4603377404407810366309201
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OFFSET
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0,3
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COMMENTS
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Special values of the hypergeometric function 3F3: a(n) = n!*binomial(n+1,n-1) * hypergeom([ -n+1, 1/2*n+1, 1/2*n+3/2], [4/3, 5/3, 2], -4/27) for n>0.
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LINKS
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FORMULA
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E.g.f.: exp(x/(1-x)^3).
a(n) ~ 1/2*exp(-1/27-n^(1/4)*3^(3/4)/72+sqrt(3*n)/6+4/3*n^(3/4)*3^(1/4)-n)*3^(1/8)*n^(n-1/8). - Vaclav Kotesovec, Jun 27 2013
a(n) = n! * Sum_{k=0..n} binomial(n+2*k-1,n-k)/k!. - Seiichi Manyama, Mar 06 2023
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MATHEMATICA
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CoefficientList[Series[E^(x/(1-x)^3), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
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PROG
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(PARI)
x='x+O('x^33);
Vec(serlaplace(exp( x/(1-x)^3 )))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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