A357265 - OEIS

%I #9 Sep 21 2022 14:10:15

%S 0,0,2,3,32,150,1884,16380,249808,3255336,59596560,1037413080,

%T 22432698144,486784686960,12233449250736,316660035739320,

%U 9111729094222080,273147758526888000,8880267446524694016,301952732236006556160,10963551960785051470080

%N Expansion of e.g.f. -LambertW(x * log(1-x)).

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

%F a(n) = n! * Sum_{k=1..floor(n/2)} k^(k-1) * |Stirling1(n-k,k)|/(n-k)!.

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

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

%Y Cf. A052807, A355842, A357267.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 21 2022