A355180 - OEIS

%I #17 Sep 24 2022 08:16:12

%S 0,0,0,0,4,10,20,35,6776,60564,352920,1663365,126625180,2361079006,

%T 27334747804,245495250455,11174333090480,328952158255400,

%U 6245314009946736,90576650639967369,3209305759254634740,122557203047084965810,3365068665450300234580

%N Expansion of e.g.f. -LambertW(x^3 * (1 - exp(x)))/6.

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

%F a(n) = (n!/6) * Sum_{k=1..floor(n/4)} k^(k-1) * Stirling2(n-3*k,k)/(n-3*k)!.

%o (PARI) my(N=20, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(serlaplace(-lambertw(x^3*(1-exp(x)))/6)))

%o (PARI) a(n) = n!*sum(k=1, n\4, k^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!)/6;

%Y Cf. A048802, A355179, A357267.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 24 2022