A371039 - OEIS

%I #13 Mar 09 2024 08:16:19

%S 1,1,2,12,72,480,4680,52920,645120,9313920,153014400,2720995200,

%T 53428636800,1154333980800,26847281260800,671610658118400,

%U 18064388076134400,517898679679180800,15763026427487539200,508612525689235968000,17329554246181072896000

%N E.g.f. satisfies A(x) = exp(x^3*A(x)) / (1-x).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

%F E.g.f.: LambertW( -x^3/(1-x) ) / (-x^3).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(n-2*k,n-3*k)/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(lambertw(-x^3/(1-x))/(-x^3)))

%o (PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(n-2*k, n-3*k)/k!);

%Y Cf. A352410, A371038.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 09 2024