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 A386937 #13 Aug 19 2025 04:22:59
%S A386937 1,5,38,325,2934,27314,259356,2496813,24281510,237978598,2346750900,
%T A386937 23257207714,231438363324,2311082461380,23146003391352,
%U A386937 232402586792061,2338665721556742,23579860411878110,238157209512898500,2409099858256570710,24403155769842168660
%N A386937 a(n) = Sum_{k=0..n} binomial(3*n+1,k) * binomial(2*n-k-1,n-k).
%F A386937 a(n) = [x^n] (1+x)^(3*n+1)/(1-x)^n.
%F A386937 a(n) = [x^n] 1/((1-x)^(n+2) * (1-2*x)^n).
%F A386937 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * binomial(3*n+1,k) * binomial(2*n-k+1,n-k).
%F A386937 a(n) = Sum_{k=0..n} 2^k * binomial(n+k-1,k) * binomial(2*n-k+1,n-k).
%F A386937 D-finite with recurrence n*(n+1)*a(n) +42*n*(n-2)*a(n-1) +12*(-33*n^2+120*n-95)*a(n-2) +72*(-63*n^2+189*n-110)*a(n-3) +3456*(3*n-8)*(3*n-10)*a(n-4)=0. - _R. J. Mathar_, Aug 19 2025
%o A386937 (PARI) a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(2*n-k-1, n-k));
%Y A386937 Cf. A091527, A386833.
%K A386937 nonn
%O A386937 0,2
%A A386937 _Seiichi Manyama_, Aug 10 2025