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 A002073 Numerators of coefficients in an asymptotic expansion of the confluent hypergeometric function F(1-b; 2; 4b). (Formerly M2268 N0897) 1
 1, -3, 3, 2, -48, -362, -49711, 13952, 574406627, 64140842, -841796802304, -326397876886, -23544490420768844, 45123679545344, 449339765798227104271, 17766371321955738181048, -20395677580116057792512, -74026374065532274752108118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Table of n, a(n) for n=0..17. Peter Henrici, Automatic computations with power series, J. Assoc. Comput. Mach. 3 (1956), 10-15. FORMULA Let f(x) = [Sum_{k>=1}(3/(2*k+1)) * x^(2*k+1)]^(1/3) = x + (1/5)*x^3 + (18/175) * x^5 + ...; let g(x) be the Lagrange inversion of f(x), g(x) = REVERT(f(x)) = 1 - (1/5) * x^3 + (3/175) * x^5 + .... Then a(n) = numerator((2 * n + 1) * coeff(g(x), 2*n+1)). - Sean A. Irvine, Jun 20 2013 MATHEMATICA nmax = 17; S = Sum[(3/(2k+1)) x^(2k+1), {k, 1, Infinity}]^(1/3) + O[x]^(3nmax) // Normal // Simplify[#, x > 0]& // InverseSeries[# + O[x]^(3nmax), x]&; a[n_] := Numerator[(2n+1) SeriesCoefficient[S, {x, 0, 2n+1}]]; a /@ Range[0, nmax] (* Jean-François Alcover, Oct 01 2020 *) CROSSREFS Cf. A002074 (denominators). Sequence in context: A196544 A289893 A265466 * A247093 A329273 A130719 Adjacent sequences: A002070 A002071 A002072 * A002074 A002075 A002076 KEYWORD sign AUTHOR N. J. A. Sloane EXTENSIONS More terms from Sean A. Irvine, Jun 20 2013 STATUS approved

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Last modified September 17 23:36 EDT 2024. Contains 375991 sequences. (Running on oeis4.)