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 A381181 #12 Feb 16 2025 10:06:41
%S A381181 1,1,2,5,8,-79,-1584,-20539,-223616,-1855295,-1736960,435730789,
%T A381181 14511117312,338965239601,6202042886144,71638247035109,
%U A381181 -714560796196864,-84697775518956799,-3650903032332091392,-115829159202293866939,-2739961030150105333760,-29414406825401517785039
%N A381181 Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + sin(x)) ).
%H A381181 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381181 E.g.f. A(x) satisfies A(x) = 1 + sin(x * A(x)).
%F A381181 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(n+1,k) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381181 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381181 a(n) = sum(k=0, n, k!*binomial(n+1, k)*I^(n-k)*a136630(n, k))/(n+1);
%Y A381181 Cf. A201627, A381180, A381182.
%Y A381181 Cf. A162653, A381171, A381173.
%Y A381181 Cf. A136630, A196776.
%K A381181 sign
%O A381181 0,3
%A A381181 _Seiichi Manyama_, Feb 16 2025