A362482 - OEIS

%I #12 Apr 22 2023 10:32:11

%S 1,1,1,1,-23,-599,-8999,-104999,-868559,5246641,582598801,21205760401,

%T 571129277401,11475082596121,81837031796521,-7904119577117399,

%U -596529385424263199,-28051840646006771999,-991870986521074646879,-21837506791918601443679

%N E.g.f. satisfies A(x) = exp(x - x^4 * A(x)^4).

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

%F E.g.f.: exp(x - LambertW(4*x^4 * exp(4*x))/4) = ( LambertW(4*x^4 * exp(4*x))/(4*x^4) )^(1/4).

%F a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k * (4*k+1)^(n-3*k-1) / (k! * (n-4*k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(4*x^4*exp(4*x))/4)))

%Y Cf. A362480, A362481.

%Y Cf. A362431, A362473.

%K sign

%O 0,5

%A _Seiichi Manyama_, Apr 21 2023