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 A386900 #14 Aug 07 2025 08:34:17
%S A386900 1,14,235,4178,76495,1426184,26922076,512838410,9837067951,
%T A386900 189729498350,3675700225435,71474375851640,1394164222173700,
%U A386900 27266825345422352,534510606516137920,10499123975453808698,206595710100771337327,4071693103719194746250
%N A386900 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(3*n+1,k).
%F A386900 a(n) = [x^n] (1+3*x)^(3*n+1)/(1-2*x).
%F A386900 a(n) = [x^n] 1/((1-3*x)^(2*n+1) * (1-5*x)).
%F A386900 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(3*n+1,k) * binomial(3*n-k,n-k).
%F A386900 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(3*n-k,n-k).
%F A386900 a(n) ~ 3^(4*n + 5/2) / (sqrt(Pi*n) * 2^(2*n+3)). - _Vaclav Kotesovec_, Aug 07 2025
%t A386900 Table[Sum[3^k*2^(n-k)*Binomial[3*n+1, k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Aug 07 2025 *)
%o A386900 (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(3*n+1, k));
%Y A386900 Cf. A386830, A386899.
%K A386900 nonn
%O A386900 0,2
%A A386900 _Seiichi Manyama_, Aug 07 2025