A362653 E.g.f. satisfies A(x) = exp( x * exp(x^2) * A(x)^2 ).

1, 1, 5, 55, 849, 17641, 462373, 14651295, 545025281, 23291218801, 1124589371301, 60553038168679, 3597677815336465, 233810179507710105, 16499939198003013509, 1256544674435523638671, 102713141497515307408257, 8970278754666722087785825

Offset: 0

Author

Seiichi Manyama, Apr 28 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A360547, A362654, A362673.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*exp(x^2))/2)))

Formula

E.g.f.: exp( -LambertW(-2*x * exp(x^2))/2 ).

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-4*k+1)^(n-2*k-1) / (k! * (n-2*k)!).