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 A381174 #11 Feb 16 2025 09:41:12
%S A381174 1,1,4,27,264,3365,52800,980903,20984320,506078505,13525493760,
%T A381174 394758794419,12414039171072,414990179398093,14523823020621824,
%U A381174 521523225315049215,18594912994237808640,613842569215361446097,14735570097970682265600,-228398321523777856462261
%N A381174 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*cos(x)) ).
%C A381174 As stated in the comment of A185951, A185951(n,0) = 0^n.
%H A381174 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A381174 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cos(x * A(x)) ).
%F A381174 a(n) = Sum_{k=0..n} k! * binomial(n+k+1,k)/(n+k+1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381174 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381174 a(n) = sum(k=0, n, k!*binomial(n+k+1, k)/(n+k+1)*I^(n-k)*a185951(n, k));
%Y A381174 Cf. A381173, A381175, A381176.
%Y A381174 Cf. A185951.
%K A381174 sign
%O A381174 0,3
%A A381174 _Seiichi Manyama_, Feb 16 2025