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 A386764 #21 Aug 03 2025 07:48:38
%S A386764 1,13,319,8872,260511,7885793,243404884,7615561092,240662849871,
%T A386764 7663737420223,245529092332599,7904950462600512,255541233005365956,
%U A386764 8289112264436610828,269663237466343607464,8794852773491081069132,287467221911677590185391,9414259968096351504747483
%N A386764 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(2*n+k-1,k).
%F A386764 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(3*n,k) * binomial(3*n-k-1,n-k).
%F A386764 a(n) = [x^n] ( (1+3*x)^3/(1-2*x)^2 )^n.
%F A386764 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-2*x)^2 / (1+3*x)^3 ). See A386770.
%F A386764 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(3*n,k).
%F A386764 a(n) = (27/4)^n - 5^n*binomial(3*n-1, n)*(hypergeom([1, 3*n], [1+n], 5/3) - 1). - _Stefano Spezia_, Aug 02 2025
%o A386764 (PARI) a(n) = sum(k=0, n, 5^k*3^(n-k)*binomial(2*n+k-1, k));
%Y A386764 Cf. A386763, A386765.
%Y A386764 Cf. A384950, A386770.
%K A386764 nonn
%O A386764 0,2
%A A386764 _Seiichi Manyama_, Aug 02 2025