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 A381520 #12 Feb 26 2025 06:26:26
%S A381520 1,1,4,27,240,2345,17280,-226597,-21007616,-1007159823,-42976972800,
%T A381520 -1775328986981,-72123329507328,-2843431148886887,-103621659777126400,
%U A381520 -2971936506262036965,-6719764584265482240,9528526268302653725537,1192610999728818101551104
%N A381520 Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + x * cos(x))^2 ) )^(1/2).
%C A381520 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381520 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381520 E.g.f. A(x) satisfies A(x) = 1 + x*A(x)^2 * cos(x*A(x)^2).
%F A381520 a(n) = (1/(2*n+1)) * Sum_{k=0..n} k! * binomial(2*n+1,k) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381520 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381520 a(n) = sum(k=0, n, k!*binomial(2*n+1, k)*I^(n-k)*a185951(n, k))/(2*n+1);
%Y A381520 Cf. A185951, A381378, A381447, A381479.
%K A381520 sign
%O A381520 0,3
%A A381520 _Seiichi Manyama_, Feb 26 2025