This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370376 #15 Mar 29 2025 07:09:21
%S A370376 1,1,6,39,262,1791,12372,86052,601374,4217151,29648766,208855791,
%T A370376 1473509736,10408539844,73596075552,520797997464,3687846866382,
%U A370376 26128671296127,185209915856802,1313356295909877,9316374980571702,66105343198654407,469174119885678972
%N A370376 Number of compositions of n where there are A025174(k) sorts of part k.
%F A370376 G.f.: 1 / (1 - 1/3 * Sum_{k>=1} binomial(3*k,k) * x^k).
%F A370376 a(0) = 1; a(n) = 1/3 * Sum_{k=1..n} binomial(3*k,k) * a(n-k).
%o A370376 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, binomial(3*k, k)*x^k)/3))
%Y A370376 Cf. A005809, A025174, A049027, A370375.
%K A370376 nonn,easy
%O A370376 0,3
%A A370376 _Seiichi Manyama_, Feb 16 2024