cp's OEIS Frontend

A349505 E.g.f. satisfies: A(x) = (1 + x)^(A(x)^3).

%I A349505 #23 Nov 21 2021 02:48:38
%S A349505 1,1,6,81,1668,46740,1659102,71386602,3611376360,210083758704,
%T A349505 13817649943440,1013979735381888,82134894774767832,
%U A349505 7279520816638839600,700730732176038359208,72803537907677356262760,8120227815636769492383168
%N A349505 E.g.f. satisfies: A(x) = (1 + x)^(A(x)^3).
%H A349505 Seiichi Manyama, <a href="/A349505/b349505.txt">Table of n, a(n) for n = 0..336</a>
%F A349505 a(n) = Sum_{k=0..n} (3*k+1)^(k-1) * Stirling1(n,k).
%F A349505 E.g.f. A(x) = Sum_{k>=0} (3*k+1)^(k-1) * (log(1+x))^k / k!.
%F A349505 From _Vaclav Kotesovec_, Nov 20 2021: (Start)
%F A349505 E.g.f.: (-LambertW(-3*log(1 + x)) / (3*log(1 + x)))^(1/3).
%F A349505 a(n) ~ n^(n-1) / (sqrt(3) * (exp(exp(-1)/3) - 1)^(n - 1/2) * exp(n + exp(-1)/6 - 5/6)). (End)
%t A349505 nmax = 20; CoefficientList[Series[(-LambertW[-3*Log[1 + x]]/(3*Log[1 + x]))^(1/3), {x, 0, nmax}], x]*Range[0, nmax]! (* _Vaclav Kotesovec_, Nov 20 2021 *)
%o A349505 (PARI) a(n) = sum(k=0, n, (3*k+1)^(k-1)*stirling(n, k, 1));
%o A349505 (PARI) N=20; x='x+O('x^N); Vec(serlaplace(sum(k=0, N, (3*k+1)^(k-1)*log(1+x)^k/k!)))
%Y A349505 Cf. A008275, A033917, A264408, A349504, A349525.
%K A349505 nonn
%O A349505 0,3
%A A349505 _Seiichi Manyama_, Nov 20 2021