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%I #10 Oct 15 2020 13:27:35
%S 1,1,2,14,224,5536,184576,7764352,394918784,23579517824,1617167879936,
%T 125302954690816,10826107873964032,1032042586785624064,
%U 107609913261744349184,12183253948487768907776,1488445213610069857796096,195181881537478283036065792,27344175437591659820860309504
%N E.g.f. A(x) satisfies: A(x) = 1 + Integral (x/A(x)^3)' / (x/A(x)^4)' dx.
%H Vaclav Kotesovec, <a href="/A338187/b338187.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ 3^(2*n - 5/4) * n^(n-2) / (2^(5/3) * exp(n - 1/6)).
%t nmax = 20; A = 1; Do[A = 1 + Integrate[D[x/A^3, x]/D[x/A^4, x], x] + O[x]^nmax, nmax]; CoefficientList[A, x] * Range[0, nmax - 1]!
%o (PARI) {a(n) = my(A=1); for(i=1, n, A = 1 + intformal( (x/A^3)'/(x/A^4 +x*O(x^n))' ); ); n!*polcoeff(A, n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A302701, A303064, A338163, A338188, A338193, A338194.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Oct 15 2020
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