A362736 - OEIS

%I #15 May 01 2023 11:28:50

%S 1,1,1,4,-3,96,-755,10368,-147623,2492416,-47137959,996741120,

%T -23260103339,594198429696,-16492683271259,494278721929216,

%U -15908038836914895,547238863907586048,-20038031401448021327,778147549666716155904,-31943565308583934360019

%N E.g.f. satisfies A(x) = exp(x^2 + x / A(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.: x / LambertW(x*exp(-x^2)) = exp( x^2 + LambertW(x*exp(-x^2)) ).

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2+lambertw(x*exp(-x^2)))))

%Y Cf. A362693, A362737.

%Y Cf. A362690.

%K sign

%O 0,4

%A _Seiichi Manyama_, May 01 2023