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 A386616 #24 Jul 29 2025 08:39:27
%S A386616 0,1,19,315,5000,77785,1196667,18282742,278031900,4214278350,
%T A386616 63723788295,961789682008,14495501585664,218216042892175,
%U A386616 3281961694927950,49322417450239980,740753733463215604,11118981305235476010,166821561372208253850,2501861335268901337425,37507747177968865536840
%N A386616 a(n) = Sum_{k=0..n-1} binomial(6*k+1,k) * binomial(6*n-6*k,n-k-1).
%F A386616 G.f.: g^3 * (g-1)/(6-5*g)^2 where g=1+x*g^6.
%F A386616 G.f.: g/((1-g)^2 * (1-6*g)^2) where g*(1-g)^5 = x.
%F A386616 a(n) = Sum_{k=0..n-1} binomial(6*k+1+l,k) * binomial(6*n-6*k-l,n-k-1) for every real number l.
%F A386616 a(n) = Sum_{k=0..n-1} 5^(n-k-1) * binomial(6*n+2,k).
%F A386616 a(n) = Sum_{k=0..n-1} 6^(n-k-1) * binomial(5*n+k+2,k).
%o A386616 (PARI) a(n) = sum(k=0, n-1, binomial(6*k+1, k)*binomial(6*n-6*k, n-k-1));
%Y A386616 Cf. A079679, A386368, A386567, A386615.
%Y A386616 Cf. A006419, A386612, A386614, A386617.
%K A386616 nonn
%O A386616 0,3
%A A386616 _Seiichi Manyama_, Jul 27 2025