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A367736 a(0) = 1; for n > 0, a(n) is the coefficient of x^a(n-1) in the expansion of Product_{k=0..n-1} (x^a(k) + 1 + 1/x^a(k)).

%I A367736 #28 Feb 05 2024 20:21:06
%S A367736 1,1,2,4,6,11,19,32,58,97,163,290,501,856,1483,2561,4424,7652,13273,
%T A367736 23024,39784,69001,119614,207042,358746,621117,1075865,1864050,
%U A367736 3227724,5590548,9682402,16770033,29049713,50310453,87142439,150939346,261424583,452810957
%N A367736 a(0) = 1; for n > 0, a(n) is the coefficient of x^a(n-1) in the expansion of Product_{k=0..n-1} (x^a(k) + 1 + 1/x^a(k)).
%t A367736 a[0] = 1; a[n_] := a[n] = Coefficient[Product[x^a[k] + 1 + 1/x^a[k], {k, 0, n - 1}], x, a[n - 1]]; Table[a[n], {n, 0, 28}]
%o A367736 (Python)
%o A367736 from itertools import islice
%o A367736 from collections import Counter
%o A367736 def A367736_gen(): # generator of terms
%o A367736     c, b = {0:1}, 1
%o A367736     while True:
%o A367736         yield b
%o A367736         d = Counter(c)
%o A367736         for k in c:
%o A367736             e = c[k]
%o A367736             d[k+b] += e
%o A367736             d[k-b] += e
%o A367736         c = d
%o A367736         b = c[b]
%o A367736 A367736_list = list(islice(A367736_gen(),20)) # _Chai Wah Wu_, Feb 05 2024
%Y A367736 Cf. A063890, A265853, A316706.
%K A367736 nonn,more
%O A367736 0,3
%A A367736 _Ilya Gutkovskiy_, Jan 24 2024
%E A367736 a(29)-a(37) from _Chai Wah Wu_, Feb 05 2024