A362431 E.g.f. satisfies A(x) = exp(x - x^4 * A(x)).
1, 1, 1, 1, -23, -239, -1439, -6719, 33601, 1536193, 24171841, 268424641, 1144566721, -47515765439, -1727426116415, -36344982098879, -481057514071679, 1197767242412161, 319851095455612801, 12145632936380316289, 293167011107091899521, 3520557699737168603521
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^4*exp(x)))))
Formula
E.g.f.: exp(x - LambertW(x^4 * exp(x))) = LambertW(x^4 * exp(x))/x^4.
a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * (k+1)^(n-3*k-1) / (k! * (n-4*k)!).