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%I #20 Jan 31 2015 17:01:10
%S 0,1,2,8,44,312,2772,30024,385688,5737232,96959396,1834244296,
%T 38390799592,880648730416,21968596282440,592083291341520,
%U 17144219069647920,530774988154571040,17495673315094986180,611738880367145595720,22614424027640541372360
%N Cumulated number of increasing admissible cuts of rooted plane trees of size n.
%C In concurrency theory, a(n) is also the cumulated sizes of computation trees induced by interleaved concurrent processes of size n.
%D O. Bodini, A. Genitrini and F. Peschanski. Enumeration and Random Generation of Concurrent Computations. In proc. 23rd International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA'12), Discrete Mathematics and Theoretical Computer Science, pp 83-96, 2012.
%H O. Bodini, A. Genitrini, F. Peschanski, <a href="http://arxiv.org/abs/1407.1873">A Quantitative Study of Pure Parallel Processes</a>, arXiv preprint arXiv:1407.1873, 2014
%F P-recurrence: (16*n-64*n^3)*a(n)+(12+72*n+112*n^2+32*n^3)*a(n+1)+(-26-62*n-4*n^3-36*n^2)*a(n+2)+(5+7*n+2*n^2)*a(n+3) = 0; a(0)=0; a(1)=1; a(2)=2.
%F a(n) ~ 2^(n-1/2) * n^(n-1) / exp(n-1). - _Vaclav Kotesovec_, Mar 08 2014
%t Flatten[{0,RecurrenceTable[{-16*(-3+n)*(-7+2*n)*(-5+2*n)*a[-3+n]+4*(-5+2*n)*(3-12*n+4*n^2)*a[-2+n]-2*(28-23*n+2*n^3)*a[-1+n]+(-2+n)*(-1+2*n)*a[n]==0,a[1]==1,a[2]==2,a[3]==8},a,{n,1,20}]}] (* _Vaclav Kotesovec_, Mar 08 2014 *)
%o (Python)
%o def a(n):
%o if n < 3:
%o return n
%o l = [0,1,2]
%o for i in range(n-2):
%o l[i%3] = ( (16*i-64*i**3)*l[i%3]+(12+72*i+112*i**2+32*i**3)*l[(i+1)%3]+(-26-62*i-4*i**3-36*i**2)*l[(i+2)%3] ) / (-5-7*i-2*i**2)
%o return l[i%3]
%Y Cf. A007852.
%K nonn
%O 0,3
%A _Antoine Genitrini_, Mar 14 2013
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