A365040 - OEIS

%I #12 Feb 16 2025 08:34:06

%S 1,1,-3,34,-623,15636,-499277,19382686,-886663647,46716323752,

%T -2786249779829,185574001203834,-13652735530485647,

%U 1099602989008154476,-96230900016000250269,9092834662610587023286,-922622745817066477888703,100054409045940667152740304

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

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

%F E.g.f.: exp( LambertW(3*x * (1+x))/3 ).

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

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

%Y Cf. A362771, A362773, A363478, A365038, A365039.

%Y Cf. A361069.

%K sign,easy,changed

%O 0,3

%A _Seiichi Manyama_, Aug 18 2023