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 A386765 #21 Aug 03 2025 12:36:25
%S A386765 1,18,624,24432,1008876,42927318,1862060124,81862383432,3634739070876,
%T A386765 162615605774568,7319222860673124,331046648931192432,
%U A386765 15033834910528707876,685059700337659528068,31307482174782491223624,1434354449577159551751432,65858845473746133806094876
%N A386765 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(3*n+k-1,k).
%F A386765 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(4*n,k) * binomial(4*n-k-1,n-k).
%F A386765 a(n) = [x^n] ( (1+3*x)^4/(1-2*x)^3 )^n.
%F A386765 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)^3 / (1+3*x)^4 ). See A386771.
%F A386765 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(4*n,k).
%F A386765 a(n) = (-2)^(-3*n)*81^n - 5^n*binomial(4*n - 1, n)*(hypergeom([1, 4*n], [1+n], 5/3) - 1). - _Stefano Spezia_, Aug 03 2025
%o A386765 (PARI) a(n) = sum(k=0, n, 5^k*3^(n-k)*binomial(3*n+k-1, k));
%Y A386765 Cf. A386763, A386764.
%Y A386765 Cf. A385438, A386771.
%K A386765 nonn
%O A386765 0,2
%A A386765 _Seiichi Manyama_, Aug 02 2025