A281431 E.g.f. S(x) satisfies: S(x) = Integral (1 + S(x)^2)^3 dx.
1, 6, 216, 19296, 3200256, 849678336, 329902212096, 176210323070976, 123889924672782336, 110895584511900450816, 123119226530619884568576, 166015794146482719037587456, 267231655288799665792971964416, 506138971421813256899173596266496, 1114219301421887004276203102410899456, 2821068813384522963411318522740301889536, 8139956209849296948206537756832040061239296
Offset: 1
Keywords
Programs
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Mathematica
terms = 20; max = 2 terms; se = (1/8)*((x*(5+3x^2))/(1+x^2)^2+3*ArcTan[x]) +O[x]^max; coes = CoefficientList[InverseSeries[se, x], x]*Range[0, max-1 ]!; Partition[coes, 2][[All, 2]] (* Jean-François Alcover, Mar 01 2017 *)
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PARI
{a(n) = my(S=x, C=1); for(i=1, n, S = intformal( C^6 +x*O(x^(2*n))); C = 1 + intformal( S*C^5 ) ); (2*n-1)!*polcoeff(S, 2*n-1)} for(n=1, 30, print1(a(n), ", "))
Formula
C(x)^2 - S(x)^2 = 1 and S'(x) = C(x)^6, where C(x) is described by A281432.