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%I #14 Apr 23 2022 01:34:31
%S 1,2,10,80,874,12092,202384,3973580,89515690,2275453700,64418414380,
%T 2009835207800,68512342137040,2533368817192280,100991942945221660,
%U 4317627768285138020,197054129197204173610,9562339765515442736180
%N Eigensequence of a sequence transformation.
%C G.f. A(x) satisfies A(x)=(A(0)+A(x/(1-x)^2)(1+x)/(1-x))/2.
%H Vaclav Kotesovec, <a href="/A048286/b048286.txt">Table of n, a(n) for n = 0..300</a>
%H Octavio Arizmendi, Takahiro Hasebe, and Franz Lehner, <a href="https://arxiv.org/abs/2204.00072">Cyclic independence: Boolean and monotone</a>, arXiv:2204.00072 [math.PR], 2022.
%H C. J. Smyth, <a href="http://www.ams.org/journals/mcom/1984-42-166/S0025-5718-1984-0736460-5/">The mean values of algebraic integers</a>, Math. Comp 42 (1984), 663-681; see eqs. (5.4), (5.8), (5.12).
%F a(n) ~ c * 2^n * n^(n + 1/2 - log(2)/4) / (exp(n) * (log(2))^n), where c = 1.64631699329139900560839601704146775549945357007201882... . - _Vaclav Kotesovec_, Aug 08 2014
%o (PARI) a(n)=local(A); if(n<1,n==0,A=1; for(k=1,n,A=1+Pol(subst(A+x*O(x^k),x,x/(1-x)^2)*(1+x)/(1-x))-A); polcoeff(A,n))
%K nonn
%O 0,2
%A _Christopher J. Smyth_
%E Edited by _Michael Somos_, Sep 24 2003
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