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A362301
a(n) = n! * Sum_{k=0..floor(n/3)} n^k * binomial(n-2*k,k)/(n-2*k)!.
6
1, 1, 1, 19, 97, 301, 13681, 124951, 647809, 46543897, 612367201, 4447574011, 436897375201, 7505523945349, 70104150466897, 8735878156045951, 185209511009456641, 2114594302777738801, 319284313084581674689, 8053189772356178472547
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = A362043(n,6*n).
a(n) = n! * [x^n] exp(x + n*x^3).
E.g.f.: exp( ( -LambertW(-3*x^3)/3 )^(1/3) ) / (1 + LambertW(-3*x^3)).
a(n) ~ (1 + 2*cos(2*Pi*mod(n,3)/3 - 3^(1/6)/2)*exp(-3^(2/3)/2)) * 3^(n/3 - 1/2) * n^n / exp(2*n/3 - 1/3^(1/3)). - Vaclav Kotesovec, Apr 18 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((-lambertw(-3*x^3)/3)^(1/3))/(1+lambertw(-3*x^3))))
CROSSREFS
Cf. A362043.
Sequence in context: A041696 A277977 A080187 * A142170 A069593 A299733
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 15 2023
STATUS
approved