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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

Table of n, a(n) for n=1..25.

N. J. A. Sloane, Transforms

Index entries for reversions of series

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

N. J. A. Sloane, Mira Bernstein

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.)