A362773 E.g.f. satisfies A(x) = exp( x * (1+x) * A(x)^2 ).

1, 1, 7, 79, 1377, 32161, 947623, 33746511, 1410518273, 67714577857, 3672410420871, 222082390164559, 14817864737168353, 1081393797641087841, 85691459902207874471, 7327398378967991154511, 672511583942513406768897, 65943097191889528063033729

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 * (1+x))/2 ).

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

From Vaclav Kotesovec, Nov 10 2023: (Start)

E.g.f.: sqrt(LambertW(-2*x * (1+x))/(-2*x * (1+x))).

a(n) ~ sqrt(-sqrt(1 + 2*exp(-1)) + 1 + 2*exp(-1)) * 2^(n-1) * n^(n-1) / ((-1 + sqrt(1 + 2*exp(-1)))^n * exp(n-1)). (End)

Mathematica

nmax = 20; CoefficientList[Series[Sqrt[LambertW[-2*x * (1+x)]/(-2*x * (1+x))], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 10 2023 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-2*x*(1+x))/2)))

Crossrefs

Cf. A047974, A362771.

Cf. A361065.

Sequence in context: A365039 A375173 A365782 * A235370 A098105 A201301

Adjacent sequences: A362770 A362771 A362772 * A362774 A362775 A362776

Keyword

nonn

Author

Seiichi Manyama, May 02 2023

Status

approved