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 A386869 #10 Aug 19 2025 04:24:21
%S A386869 1,11,168,2839,50333,917604,17036260,320383295,6082829067,
%T A386869 116342007859,2238247173440,43266114873636,839661737871388,
%U A386869 16349646755219432,319263686177979564,6249714381417109903,122603983720769666087,2409746305286188995681
%N A386869 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(3*n+2,k) * binomial(3*n-k,n-k).
%F A386869 a(n) = [x^n] (1+x)^(3*n+2)/(1-2*x)^(2*n+1).
%F A386869 a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^(2*n+1)).
%F A386869 a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(3*n+2,k).
%F A386869 a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(2*n+k,k).
%F A386869 D-finite with recurrence 544*n*(2*n-1)*a(n) +8*(618*n^2-9184*n+8025)*a(n-1) +2*(-276538*n^2+1112059*n-1061145)*a(n-2) +15327*(3*n-4)*(3*n-5)*a(n-3)=0. - _R. J. Mathar_, Aug 19 2025
%o A386869 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(3*n+2, k)*binomial(3*n-k, n-k));
%Y A386869 Cf. A385667, A386844.
%K A386869 nonn
%O A386869 0,2
%A A386869 _Seiichi Manyama_, Aug 06 2025