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%I #4 Jan 22 2024 05:55:21
%S 1,1,1,1,1,1,1,1,1,19,28,41,60,88,129,189,277,406,595,872,1278,1873,
%T 2745,4023,5896,8641,12664,18560,27201,39865,58425,85626,125491,
%U 183916,269542,395033,2823330,4343681,6682741,10281375,15817857,24335721,37440426,57601964
%N Number of compositions (ordered partitions) of n into triangular numbers not greater than sqrt(n).
%t Table[SeriesCoefficient[1/(1 - Sum[x^(k (k + 1)/2), {k, 1, Floor[(Sqrt[1 + 8 Sqrt[n]] - 1)/2]}]), {x, 0, n}], {n, 0, 43}]
%Y Cf. A023361, A364526.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Jan 20 2024
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