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 A386767 #16 Aug 03 2025 10:59:57
%S A386767 1,12,294,8178,240186,7271832,224484684,7024333608,221997758346,
%T A386767 7069839153252,226514542354974,7293106513777338,235771657829954856,
%U A386767 7648097463209959872,248816951694728297664,8115177647328907792368,265257523746851227499466,8687091365891501763853692
%N A386767 a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(2*n+k-1,k).
%F A386767 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(3*n,k) * binomial(3*n-k-1,n-k).
%F A386767 a(n) = [x^n] ( (1+2*x)^3/(1-3*x)^2 )^n.
%F A386767 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-3*x)^2 / (1+2*x)^3 ). See A386773.
%F A386767 a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(3*n,k).
%F A386767 D-finite with recurrence 54*n*(2*n-1)*a(n) +3*(-2063*n^2+4087*n-2340)*a(n-1) +4*(21379*n^2-81239*n+73110)*a(n-2) +50*(277*n^2-6323*n+15702)*a(n-3) -8400*(3*n-10)*(3*n-11)*a(n-4)=0. - _R. J. Mathar_, Aug 03 2025
%o A386767 (PARI) a(n) = sum(k=0, n, 5^k*2^(n-k)*binomial(2*n+k-1, k));
%Y A386767 Cf. A386766, A386768.
%Y A386767 Cf. A386773.
%K A386767 nonn
%O A386767 0,2
%A A386767 _Seiichi Manyama_, Aug 02 2025