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 A381479 #8 Feb 25 2025 01:58:36
%S A381479 1,1,6,69,1200,28085,828240,29502473,1232606592,59114482569,
%T A381479 3201204188160,193215861134989,12862437022076928,936256855741871677,
%U A381479 73978404781917941760,6306254322850544942865,576881179288397985054720,56369243043268551691136657,5859726074013471622734938112
%N A381479 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)^2) ).
%C A381479 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381479 a(n) = Sum_{k=0..n} k! * binomial(2*n+k+1,k)/(2*n+k+1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%F A381479 E.g.f.: ( (1/x) * Series_Reversion( x*(1 - x*cos(x))^2 ) )^(1/2).
%o A381479 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381479 a(n) = sum(k=0, n, k!*binomial(2*n+k+1, k)/(2*n+k+1)*I^(n-k)*a185951(n, k));
%Y A381479 Cf. A185951, A364985, A381388.
%K A381479 nonn
%O A381479 0,3
%A A381479 _Seiichi Manyama_, Feb 24 2025