OFFSET
1,2
COMMENTS
Exponential reversion of A008578 (1 together with primes).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..200
FORMULA
a(n) ~ -(-1)^n * n^(n-1) / (sqrt(t) * r^(n - 1/2) * exp(n)), where t = Sum_{k>=0} prime(k+1) * s^k / k! = 0.7444466039931411886049681349033665583265654464..., s = -0.835708320094278846648094879804371313211261254223... is the root of the equation Sum_{k>=1} prime(k) * s^k / k! = -1 and r = -s - Sum_{k>=2} prime(k-1) * s^k / k! = 0.34673082109620141270389189466020238662524394743... - Vaclav Kotesovec, Apr 21 2020
MATHEMATICA
nmax = 19; CoefficientList[InverseSeries[Series[x + Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 20 2020
STATUS
approved