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A362734
E.g.f. satisfies A(x) = exp(x + x * A(x)^3).
7
1, 2, 16, 296, 8512, 333632, 16595200, 1001460224, 71094759424, 5805799829504, 536188352856064, 55259197654089728, 6287146625230962688, 782751635353947865088, 105852868748672770244608, 15451195442132410179780608, 2421355190097788960505856000
OFFSET
0,2
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: ( -LambertW(-3*x*exp(3*x)) / (3*x) )^(1/3) = exp( x - LambertW(-3*x*exp(3*x))/3 ).
a(n) = Sum_{k=0..n} (3*k+1)^(n-1) * binomial(n,k) = 2^n * A349714(n).
a(n) ~ sqrt(LambertW(exp(-1)) + 1) * 3^(n-1) * n^(n-1) / (exp(n) * LambertW(exp(-1))^(n + 1/3)). - Vaclav Kotesovec, Apr 24 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x*exp(3*x))/3)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 01 2023
STATUS
approved