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 A386830 #10 Aug 19 2025 03:35:05
%S A386830 1,18,459,12942,382671,11632248,360048924,11287595862,357239123631,
%T A386830 11389281564978,365227235524539,11767662196724232,380651590433357316,
%U A386830 12354006908520865008,402088229127633026304,13119017347331737771302,428955765661154879370351
%N A386830 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(3*n+1,k) * binomial(3*n-k,n-k).
%F A386830 a(n) = [x^n] (1+3*x)^(3*n+1)/(1-2*x)^(2*n+1).
%F A386830 a(n) = [x^n] 1/((1-3*x) * (1-5*x)^(2*n+1)).
%F A386830 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(3*n+1,k).
%F A386830 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(2*n+k,k).
%F A386830 Conjecture D-finite with recurrence +8*n*(2*n-3)*a(n) +6*(-108*n^2+207*n-80)*a(n-1) +405*(3*n-2)*(3*n-4)*a(n-2)=0. - _R. J. Mathar_, Aug 19 2025
%o A386830 (PARI) a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(3*n+1, k)*binomial(3*n-k, n-k));
%Y A386830 Cf. A386829, A386831.
%Y A386830 Cf. A386764.
%K A386830 nonn
%O A386830 0,2
%A A386830 _Seiichi Manyama_, Aug 05 2025