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

0,3

Links

Table of n, a(n) for n=0..17.

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

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)!).

Prog

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

Crossrefs

Cf. A360547, A362654, A362673.

Sequence in context: A132865 A294051 A145662 * A094418 A365588 A367164

Adjacent sequences: A362650 A362651 A362652 * A362654 A362655 A362656

Keyword

nonn

Author

Seiichi Manyama, Apr 28 2023

Status

approved