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A362568
E.g.f. satisfies A(x) = exp(x/A(x)^x).
2
1, 1, 1, -5, -23, 121, 1321, -7349, -148175, 853777, 27840241, -163354949, -7934320679, 46820981065, 3203091569497, -18833438286389, -1742847946697759, 10137524365568161, 1230956201929018465, -7042544858204663813, -1095864481054115534519
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: (x^2 / LambertW(x^2))^(1/x) = exp(LambertW(x^2) / x) = exp(x * exp(-LambertW(x^2))).
a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * (n-k)^k * binomial(n-k-1,k)/(n-k)!.
E.g.f.: Sum_{k>=0} (-k*x + 1)^(k-1) * x^k / k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(x^2)))))
CROSSREFS
Cf. A361777.
Sequence in context: A151881 A229811 A359915 * A121636 A361305 A200028
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 25 2023
STATUS
approved