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 A370375 #14 Mar 29 2025 07:09:24
%S A370375 1,3,24,201,1710,14649,125934,1084716,9353574,80711625,696756420,
%T A370375 6016526145,51962422464,448833782556,3877191573720,33494487646632,
%U A370375 289365173239302,2499947731531305,21598513018825920,186604716462810075,1612224571249844910
%N A370375 Number of compositions of n where there are A005809(k) sorts of part k.
%F A370375 G.f.: 1 / (1 - Sum_{k>=1} binomial(3*k,k) * x^k).
%F A370375 a(0) = 1; a(n) = Sum_{k=1..n} binomial(3*k,k) * a(n-k).
%o A370375 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, binomial(3*k, k)*x^k)))
%Y A370375 Cf. A005809, A024485, A075436, A370327, A370376.
%K A370375 nonn,easy
%O A370375 0,2
%A A370375 _Seiichi Manyama_, Feb 16 2024