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%I #19 Dec 12 2023 08:28:31
%S 1,3,11,46,210,1018,5150,26889,143829,784167,4341843,24348352,
%T 138007784,789375504,4550522248
%N Number of distinct monomials in the expansion of Product_{i=1..n} (y_1+...+y_i+x_i+x_{i+1}).
%H T. Amdeberhan, M. Alekseyev, <a href="http://mathoverflow.net/q/260017">Expanding into monomials</a>, MathOverflow, 2017.
%o (SageMath)
%o def A281548(n):
%o R.<x> = PowerSeriesRing(ZZ)
%o return sum(sum(
%o ( prod(1 + (1-2*x+O(x^(k+1)))^(-c[i]-1)
%o for i in range(n-k) )
%o ) * (1-2*x+O(x^(k+1)))^(-(n-k-sum(c))-1) / 2^(n-k)
%o for c in map(lambda t: t.to_Catalan_code(), DyckWords(n-k)) )[k]
%o for k in range(n+1) )
%Y Cf. A000108, A006318.
%K nonn,more
%O 0,2
%A _Max Alekseyev_, Jan 23 2017
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