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 A381519 #11 Feb 26 2025 06:26:17
%S A381519 1,2,10,82,936,13642,240656,4952218,115608704,2992207250,84070140672,
%T A381519 2507383885730,77117178496000,2329071118971482,61202811821836288,
%U A381519 690380688651775978,-88097620429234470912,-11900508444760552311518,-1112180862634722333884416
%N A381519 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sin(x))^2 ).
%H A381519 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381519 E.g.f. A(x) satisfies A(x) = (1 + sin(x*A(x)))^2.
%F A381519 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381518.
%F A381519 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(2*n+2,k) * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381519 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381519 a(n) = sum(k=0, n, k!*binomial(2*n+2, k)*I^(n-k)*a136630(n, k))/(n+1);
%Y A381519 Cf. A136630, A381389, A381518.
%Y A381519 Cf. A377553, A381442, A381449, A381521.
%K A381519 sign
%O A381519 0,2
%A A381519 _Seiichi Manyama_, Feb 26 2025