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 A381410 #10 Feb 23 2025 08:04:15
%S A381410 1,2,4,2,-128,-2118,-23456,-125046,2962432,134260082,3203705344,
%T A381410 43519495186,-465102608384,-58643045328086,-2434321489723392,
%U A381410 -60275924271785062,-100012292095737856,89170947715367242466,5992924139510968483840,233532153884059053483042
%N A381410 E.g.f. A(x) satisfies A(x) = exp( 2 * x * cos(x * A(x)) ).
%C A381410 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381410 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381409.
%F A381410 a(n) = 2 * Sum_{k=0..n} (2*n-2*k+2)^(k-1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381410 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381410 a(n) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*I^(n-k)*a185951(n, k));
%Y A381410 Cf. A185951, A381409.
%K A381410 sign
%O A381410 0,2
%A A381410 _Seiichi Manyama_, Feb 23 2025