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 A007296 Reversion of (1 + g.f. for primes). (Formerly M1483) 3
 1, -2, 5, -15, 52, -200, 827, -3596, 16191, -74702, 350794, -1669439, 8029728, -38963552, 190499461, -937550897, 4641253152, -23096403422, 115475977145, -579799302750, 2922325238788, -14780595276064, 74995317703482, -381625745964018, 1947147485751919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS N. J. A. Sloane, Transforms FORMULA a(n) ~ -(-1)^n / (sqrt(2*Pi*t) * n^(3/2) * r^(n - 1/2)), where t = Sum_{k>=0} (k+1)*(k+2)*prime(k+1) * s^k = 2.76855665284448835155556293964568965050630014..., s = -0.4018472849329562729164121279063799981049446018535... is the root of the equation Sum_{k>=1} (k+1)*prime(k) * s^k = -1 and r = -s - Sum_{k>=2} prime(k-1) * s^k = 0.18422249999982341975449666640383532448650252568... - Vaclav Kotesovec, Apr 21 2020 MAPLE read transforms; s1 := [seq(ithprime(i), i=1..40)]; s2 := [1, op(%)]; REVERT(%); MATHEMATICA nmax = 25; Rest[CoefficientList[InverseSeries[Series[x + Sum[Prime[k-1]*x^k, {k, 2, nmax}], {x, 0, nmax}], x], x]] (* Vaclav Kotesovec, Apr 21 2020 *) CROSSREFS Cf. A334263. Sequence in context: A287583 A287276 A007312 * A279558 A224071 A202062 Adjacent sequences:  A007293 A007294 A007295 * A007297 A007298 A007299 KEYWORD sign,easy AUTHOR EXTENSIONS Signs corrected Dec 24 2001 STATUS approved

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Last modified July 27 14:47 EDT 2021. Contains 346307 sequences. (Running on oeis4.)