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 A381518 #8 Feb 26 2025 06:26:45
%S A381518 1,1,4,29,304,4141,68832,1337881,29432576,712263961,18403873280,
%T A381518 487814777141,12296236382208,230142147098501,-2906327530115072,
%U A381518 -800177574047914831,-75835523291585773568,-6054072134316123116495,-459749417224473755910144,-34556942957229166465685555
%N A381518 Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + sin(x))^2 ) )^(1/2).
%H A381518 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381518 E.g.f. A(x) satisfies A(x) = 1 + sin(x*A(x)^2).
%F A381518 a(n) = (1/(2*n+1)) * Sum_{k=0..n} k! * binomial(2*n+1,k) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381518 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381518 a(n) = sum(k=0, n, k!*binomial(2*n+1, k)*I^(n-k)*a136630(n, k))/(2*n+1);
%Y A381518 Cf. A136630, A198865, A381519.
%K A381518 sign
%O A381518 0,3
%A A381518 _Seiichi Manyama_, Feb 26 2025