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A127897
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Series reversion of x/(1+2x+3x^2+x^3).
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2
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0, 1, 2, 7, 27, 114, 507, 2342, 11125, 54002, 266684, 1335610, 6767477, 34629709, 178701317, 928903447, 4859345882, 25563551782, 135153617840, 717740916202, 3826894116962, 20478451476328, 109945087353190
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OFFSET
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0,3
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COMMENTS
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Series reversion of A127896.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
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G.f.: 2*sqrt(3)*sqrt((1+x)/x)*sin(asin(3*sqrt(3)/(2*sqrt((1+x)/x)))/3)/3; a(n)=sum{k=0..n-1, sum{j=0..k, (1/(2k+j-1))*C(n-1,3k-j)*C(3k-j,k)*C(k,j)*2^(n-3k+j-1)*3^j}};
Recurrence: 2*n*(2*n+1)*a(n) = (3*n-1)*(5*n-2)*a(n-1) + 2*(n-2)*(21*n-20)*a(n-2) + 23*(n-3)*(n-2)*a(n-3). - Vaclav Kotesovec, Oct 20 2012
a(n) ~ 23^(n+1/2)/(12*4^n*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012
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MATHEMATICA
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Flatten[{0, Rest[CoefficientList[Series[2*Sqrt[3]*Sqrt[(1+x)/x]*Sin[ArcSin[3*Sqrt[3]/(2*Sqrt[(1+x)/x])]/3]/3, {x, 0, 20}], x]]}] (* Vaclav Kotesovec, Oct 20 2012 *)
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CROSSREFS
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Sequence in context: A150627 A150628 A106225 * A180473 A154108 A011965
Adjacent sequences: A127894 A127895 A127896 * A127898 A127899 A127900
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Feb 04 2007
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STATUS
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approved
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