A356927 E.g.f. satisfies A(x) = 1/(1 - x)^(A(x)/(1 - x)).

1, 1, 6, 54, 676, 10980, 220488, 5289592, 147828896, 4721152320, 169723566240, 6785559484704, 298726260001728, 14362141350822720, 748845960914596608, 42092072779399215360, 2537464961261745635328, 163317885950059143238656

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.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (-log(1-x)/(1-x))^k / k!.

E.g.f.: A(x) = exp( -LambertW(log(1-x)/(1-x)) ).

E.g.f.: A(x) = (1-x) * LambertW(log(1-x)/(1-x))/log(1-x).

a(n) ~ sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (LambertW(exp(-1)) * exp(n - 1/2) * (1 - exp(1)*LambertW(exp(-1)))^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(-log(1-x)/(1-x))^k/k!)))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(log(1-x)/(1-x)))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1-x)*lambertw(log(1-x)/(1-x))/log(1-x)))

Crossrefs

Cf. A000254, A000272, A052813, A087761, A356925.

Sequence in context: A357309 A137591 A292716 * A072034 A167571 A366232

Adjacent sequences: A356924 A356925 A356926 * A356928 A356929 A356930

Keyword

nonn

Author

Seiichi Manyama, Sep 04 2022

Status

approved