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 A384695 #12 Aug 16 2025 10:02:16
%S A384695 1,6,120,2850,72990,1950816,53594508,1500996420,42639593040,
%T A384695 1224606404670,35477155257720,1035058071490152,30375294227227530,
%U A384695 895810786837337880,26530164526824124560,788575111385154710700,23513904388397505712014,703104985574123730695460,21076207836773295148694400
%N A384695 Self-convolution square-root of A169961, where A169961(n) = binomial(12*n,n).
%F A384695 a(n) ~ 12^(12*n + 1/4) / (2^(1/4) * Gamma(1/4) * 11^(11*n + 1/4) * n^(3/4)).
%F A384695 From _Seiichi Manyama_, Aug 16 2025: (Start)
%F A384695 Sum_{k=0..n} a(k) * a(n-k) = A169961(n).
%F A384695 G.f.: 1/sqrt(1 - 12*x*g^11) where g = 1+x*g^12.
%F A384695 G.f.: sqrt( g/(12-11*g) ) where g = 1+x*g^12. (End)
%t A384695 nmax = 20; self = ConstantArray[0, nmax + 1]; self[[1]] = 1; self[[2]] = 6; Do[self[[k+1]] = (Binomial[12*k, k] - Sum[self[[j+1]]*self[[k - j + 1]], {j, 1, k-1}]) / (2*self[[1]]);, {k, 2, nmax}]; self
%Y A384695 Cf. A169961, A208977, A383965.
%K A384695 nonn
%O A384695 0,2
%A A384695 _Vaclav Kotesovec_, Jun 07 2025