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 A385670 #11 Aug 04 2025 08:02:35
%S A385670 1,17,429,12048,355501,10792737,333781044,10457735928,330823760061,
%T A385670 10543365694707,338004221112309,10887987584565108,352127854740967596,
%U A385670 11426385227977214252,371844089088280093224,12130745906826301055088,396599383187880024765981
%N A385670 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(3*n+1,k) * binomial(3*n-k,n-k).
%F A385670 a(n) = [x^n] (1+2*x)^(3*n+1)/(1-3*x)^(2*n+1).
%F A385670 a(n) = [x^n] 1/((1-2*x) * (1-5*x)^(2*n+1)).
%F A385670 a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(3*n+1,k).
%F A385670 a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(2*n+k,k).
%o A385670 (PARI) a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(3*n+1, k)*binomial(3*n-k, n-k));
%Y A385670 Cf. A385669, A385671.
%Y A385670 Cf. A386767.
%K A385670 nonn
%O A385670 0,2
%A A385670 _Seiichi Manyama_, Aug 04 2025