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A371039
E.g.f. satisfies A(x) = exp(x^3*A(x)) / (1-x).
1
1, 1, 2, 12, 72, 480, 4680, 52920, 645120, 9313920, 153014400, 2720995200, 53428636800, 1154333980800, 26847281260800, 671610658118400, 18064388076134400, 517898679679180800, 15763026427487539200, 508612525689235968000, 17329554246181072896000
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f.: LambertW( -x^3/(1-x) ) / (-x^3).
a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(n-2*k,n-3*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(-x^3/(1-x))/(-x^3)))
(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-2*k, n-3*k)/k!);
CROSSREFS
Sequence in context: A375607 A181966 A052556 * A052833 A277490 A296975
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 09 2024
STATUS
approved