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A338377 G.f. satisfies: A(x) = (1 + x * d/dx(x*A(x)) )^n.

%I A338377 #8 Oct 23 2020 10:39:25
%S A338377 1,1,9,226,10745,811026,88058362,12920344256,2453913830097,
%T A338377 584608650175630,170543970449421371,59769169004510011674,
%U A338377 24775053368568412720967,11989194513429991057937296,6698670769128767044654361520,4280089524780608663200103685056,3101341801862271814724389007080481
%N A338377 G.f. satisfies: A(x) = (1 + x * d/dx(x*A(x)) )^n.
%H A338377 Vaclav Kotesovec, <a href="/A338377/b338377.txt">Table of n, a(n) for n = 0..220</a>
%F A338377 G.f. satisfies: A(x) = (1 + x * A(x) + x^2 * A'(x) )^n.
%F A338377 a(n) ~ A238223 * exp(1) * n! * n^(n + 1 - 1/n).
%F A338377 a(n) ~ A238223 * exp(1) * n^(n+1) * n! * (1 - log(n)/n).
%e A338377 a(2) = A113662(2) = 9
%e A338377 a(3) = A113663(3) = 226
%e A338377 a(4) = A113664(4) = 10745
%e A338377 a(5) = A113665(5) = 811026
%e A338377 a(6) = A113666(6) = 88058362
%e A338377 a(7) = A113667(7) = 12920344256
%e A338377 a(8) = A113668(8) = 2453913830097
%o A338377 (PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=(1+x*deriv(x*A))^n); polcoeff(A, n, x)}
%o A338377 for(n=0, 20, print1(a(n), ", "))
%Y A338377 Cf. A113662, A113663, A113664, A113665, A113666, A113667, A113668.
%K A338377 nonn
%O A338377 0,3
%A A338377 _Vaclav Kotesovec_, Oct 23 2020