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A362173
a(n) = n! * Sum_{k=0..floor(n/3)} (n/6)^k * binomial(n-2*k,k)/(n-2*k)!.
5
1, 1, 1, 4, 17, 51, 481, 3676, 18369, 272917, 3011201, 21058236, 427112401, 6160655359, 55380250017, 1423658493076, 25361574327041, 278603741558601, 8673295084155649, 183914415577719892, 2387417408385462801, 87273239189497636171, 2146479566819857007201
OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
a(n) = n! * [x^n] exp(x + n*x^3/6).
E.g.f.: exp( ( -2*LambertW(-x^3/2) )^(1/3) ) / (1 + LambertW(-x^3/2)).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-2*lambertw(-x^3/2))^(1/3))/(1+lambertw(-x^3/2))))
CROSSREFS
Main diagonal of A362043.
Sequence in context: A228960 A370212 A131339 * A047668 A208658 A092091
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 14 2023
STATUS
approved