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%I #28 Nov 05 2021 05:28:14
%S 1,1,3,8,25,77,262,897,3208,11658,43243,162477,618219,2374699,9200541,
%T 35903017,140997527,556798525,2209685939,8807924914,35248187347,
%U 141564134395,570402287162,2305138038036,9340981510156,37946616550787
%N Permutation rooted trees with n nodes.
%H Vaclav Kotesovec, <a href="/A050383/b050383.txt">Table of n, a(n) for n = 1..240</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=773">Encyclopedia of Combinatorial Structures 773</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F G.f. (with offset 0) satisfies: A(x) = 1/Product_{n>=1} (1 - x^n*A(x^n)). - _Paul D. Hanna_, Sep 28 2011
%F Shifts left under transform T where Ta is EULER(CIK(a)).
%F a(n) ~ c * d^n / n^(3/2), where d = 4.313133937842504228... and c = 0.153549235191409889... - _Vaclav Kotesovec_, Nov 05 2021
%t m = 26; A[_] = 0;
%t Do[A[x_] = 1/Product[1 - x^n A[x^n], {n, 1, m}] + O[x]^m // Normal, {m}];
%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Oct 02 2019 *)
%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1/prod(k=1, n, (1-x^k*subst(A,x,x^k+x*O(x^n))))); polcoeff(A, n)} /* Paul D. Hanna */
%Y Cf. A004111, A005355, A091865, A308368.
%K nonn,eigen
%O 1,3
%A _Christian G. Bower_, Nov 15 1999
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