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 A381180 #7 Feb 16 2025 10:06:14
%S A381180 1,1,0,-1,-8,-19,64,1091,7680,-1415,-650752,-8575865,-35559424,
%T A381180 857890021,21380186112,203548592651,-1615715926016,-95486152906639,
%U A381180 -1599622990659584,-1397194164399601,657963431581974528,18168041375501245021,157453907927886725120,-6059840564222790027821
%N A381180 E.g.f. A(x) satisfies A(x) = 1 + sin(x*A(x)) / A(x).
%F A381180 a(n) = Sum_{k=0..n} k! * binomial(n-k+1,k)/(n-k+1) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381180 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381180 a(n) = sum(k=0, n, k!*binomial(n-k+1, k)/(n-k+1)*I^(n-k)*a136630(n, k));
%Y A381180 Cf. A201627, A381181, A381182.
%Y A381180 Cf. A136630, A196776.
%K A381180 sign
%O A381180 0,5
%A A381180 _Seiichi Manyama_, Feb 16 2025