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 A381182 #9 Feb 16 2025 10:06:36
%S A381182 1,1,6,71,1288,31661,984640,37085075,1641305472,83497838425,
%T A381182 4801347029504,307975150996831,21802395720298496,1688562016007776261,
%U A381182 142023935786330431488,12892154760586821775019,1256251152910271399624704,130793914073764385411654321,14490427167940362294881615872
%N A381182 E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sin(x * A(x)) ).
%F A381182 a(n) = Sum_{k=0..n} k! * binomial(n+2*k+1,k)/(n+2*k+1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381182 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381182 a(n) = sum(k=0, n, k!*binomial(n+2*k+1, k)/(n+2*k+1)*I^(n-k)*a136630(n, k));
%Y A381182 Cf. A201627, A381180, A381181.
%Y A381182 Cf. A136630, A196776.
%K A381182 nonn
%O A381182 0,3
%A A381182 _Seiichi Manyama_, Feb 16 2025