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 A381409 #9 Feb 23 2025 08:03:24
%S A381409 1,1,1,-2,-59,-744,-6419,-6096,1504553,47199232,911415481,7309642880,
%T A381409 -338340409043,-21607316073472,-725479564376475,-13094500078091264,
%U A381409 245361657851526353,35579148236923486208,1875350389057457406193,57582879572195726819328
%N A381409 E.g.f. A(x) satisfies A(x) = exp( x * cos(x * A(x)^2) ).
%C A381409 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381409 a(n) = Sum_{k=0..n} (2*n-2*k+1)^(k-1) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381409 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381409 a(n) = sum(k=0, n, (2*n-2*k+1)^(k-1)*I^(n-k)*a185951(n, k));
%Y A381409 Cf. A185951, A381378.
%K A381409 sign
%O A381409 0,4
%A A381409 _Seiichi Manyama_, Feb 23 2025