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%I #24 May 02 2020 16:07:39
%S 0,1,2,6,25,113,548,2770,14426,76851,416848,2294224,12780394,71924647,
%T 408310668,2335443077,13446130438,77863375126,453203435319,
%U 2649957419351,15558520126830,91687179000949,542139459641933,3215484006733932,19125017153077911
%N Number of rooted identity trees with 2n nodes.
%H Alois P. Heinz, <a href="/A299098/b299098.txt">Table of n, a(n) for n = 0..1253</a>
%F a(n) = A004111(2*n).
%e a(3) = 6:
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%p with(numtheory):
%p b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(
%p b(d)*d*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
%p end:
%p a:= n-> b(2*n):
%p seq(a(n), n=0..30);
%t b[n_] := b[n] = If[n<2, n, Sum[b[n-k]*Sum[b[d]*d*(-1)^(k/d + 1), {d, Divisors[k]}], {k, 1, n-1}]/(n-1)];
%t a[n_] := b[2*n];
%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Jun 18 2018, after _Alois P. Heinz_ *)
%o (Python)
%o from sympy import divisors
%o from sympy.core.cache import cacheit
%o @cacheit
%o def b(n): return n if n<2 else sum([b(n-k)*sum([b(d)*d*(-1)**(k//d+1) for d in divisors(k)]) for k in range(1, n)])//(n-1)
%o def a(n): return b(2*n)
%o print([a(n) for n in range(31)]) # _Indranil Ghosh_, Mar 02 2018, after Maple program
%Y Bisection of A004111 (even part).
%Y Cf. A100034, A299039, A299113.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Feb 02 2018
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