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 A386829 #10 Aug 05 2025 10:00:59
%S A386829 1,13,204,3457,61006,1103598,20299434,377871297,7097430726,
%T A386829 134243202358,2553356761264,48788507855562,935791802540596,
%U A386829 18007015501848568,347459946354962694,6720599552926105377,130263082422599127366,2529516572366126192478
%N A386829 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(2*n+1,k) * binomial(2*n-k,n-k).
%F A386829 a(n) = [x^n] (1+3*x)^(2*n+1)/(1-2*x)^(n+1).
%F A386829 a(n) = [x^n] 1/((1-3*x) * (1-5*x)^(n+1)).
%F A386829 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(2*n+1,k).
%F A386829 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(n+k,k).
%o A386829 (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(2*n+1, k)*binomial(2*n-k, n-k));
%Y A386829 Cf. A386830, A386831.
%Y A386829 Cf. A385669, A386763.
%K A386829 nonn
%O A386829 0,2
%A A386829 _Seiichi Manyama_, Aug 05 2025