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A178920
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Expansion of e.g.f. A(x), where A(x)=exp(x*A(x)+x^2*A(x)^2)
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0
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1, 4, 39, 616, 13445, 374976, 12738523, 510366592, 23561390889, 1231594508800, 71902556218031, 4637321353737216, 327439395476545261, 25123251004703358976, 2081326422827575699875
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (n-1)!*Sum_{i=0..n-1} binomial(n+i,n-i-1)*n^i/i!. - corrected by Vaclav Kotesovec, Jan 26 2014
a(n) ~ c * n^n * ( exp(m-1) * (1+m)^(1+m) / (m^(3*m) * 2^(2*m) * (1-m)^(1-m)) )^n, where m = 1/12*(-1 + (215 - 12*sqrt(321))^(1/3) + (215 + 12*sqrt(321))^(1/3)) = 0.5566930950324... is the root of the equation m^2*(1+4*m)=1, and c = 2.194433179699246977948075450550764549... - Vaclav Kotesovec, Jan 26 2014
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MATHEMATICA
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a[n_] := (n+1)!*HypergeometricPFQ[ {-n, n+2}, {1, 3/2}, -(n+1)/4]; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Mar 01 2013 *)
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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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