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A362477
E.g.f. satisfies A(x) = exp(x + x^3/6 * A(x)^3).
3
1, 1, 1, 2, 17, 161, 1351, 12391, 153385, 2388905, 40060781, 708351821, 13861042801, 305141790097, 7339275555067, 188198812659131, 5143808931521681, 150713978752271441, 4718460264313196665, 156524510548008965305, 5474266337362911068161
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(-x^3/2 * exp(3*x))/3) = ( -2 * LambertW(-x^3/2 * exp(3*x))/x^3 )^(1/3).
a(n) = n! * Sum_{k=0..floor(n/3)} (1/6)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/2*exp(3*x))/3)))
CROSSREFS
Column k=1 of A362490.
Cf. A362381.
Sequence in context: A126037 A241135 A112321 * A276198 A178806 A197864
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 21 2023
STATUS
approved