A365037 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).
1, 1, 3, -11, -11, 1341, -14339, -168923, 8905065, -85313735, -4604578919, 197455645641, -273728455571, -267002430142187, 9427821270512373, 178475402982086701, -28273343910563670959, 713736314833387866225, 51907546734507018043057
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(3*x^2*exp(-3*x))/3)))
Formula
E.g.f.: exp( x + LambertW(3*x^2*exp(-3*x))/3 ).
a(n) = n! * Sum_{k=0..n} (-3*n+3*k+1)^(k-1) * binomial(k,n-k)/k!.