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 A381173 #12 Feb 16 2025 09:41:08
%S A381173 1,1,2,3,-24,-475,-5760,-52297,-155008,8781705,313344000,6966991339,
%T A381173 102864807936,18664712365,-71473582229504,-3387816787568865,
%U A381173 -103478592573112320,-1899945146589964783,18941335827815596032,3808766537454425974739,215681241589289359769600
%N A381173 Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cos(x)) ).
%C A381173 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381173 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381173 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)) ).
%F A381173 a(n) = (1/(n+1)) * Sum_{k=0..n} k! * binomial(n+1,k) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381173 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381173 a(n) = sum(k=0, n, k!*binomial(n+1, k)*I^(n-k)*a185951(n, k))/(n+1);
%Y A381173 Cf. A381174, A381175, A381176.
%Y A381173 Cf. A162653, A381171, A381181.
%Y A381173 Cf. A185951.
%K A381173 sign
%O A381173 0,3
%A A381173 _Seiichi Manyama_, Feb 16 2025