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A362472
E.g.f. satisfies A(x) = exp(x + x^3 * A(x)^3).
4
1, 1, 1, 7, 97, 961, 10201, 177241, 3801505, 80718625, 1887205681, 52896262321, 1648697978401, 54216677033377, 1928791931034697, 75326014326206281, 3159713152034201281, 140373558362282197441, 6632746205445950124385, 333591744669464008432225
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: exp(x - LambertW(-3*x^3 * exp(3*x))/3) = ( -LambertW(-3*x^3 * exp(3*x))/(3*x^3) )^(1/3).
a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^3*exp(3*x))/3)))
CROSSREFS
Column k=6 of A362490.
Sequence in context: A219088 A116261 A289851 * A242377 A178005 A268706
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 21 2023
STATUS
approved