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 A381378 #11 Feb 22 2025 09:56:19
%S A381378 1,1,2,3,-48,-1135,-18240,-231637,-1356544,53849889,3026119680,
%T A381378 100808786419,2429052865536,26284690243825,-1539261873164288,
%U A381378 -140633348417624805,-7196339681250508800,-258335768147494234303,-4225401456668904259584,307227604973975435785571
%N A381378 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^2) ).
%C A381378 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381378 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.
%o A381378 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381378 a(n) = sum(k=0, n, k!*binomial(2*n-k+1, k)/(2*n-k+1)*I^(n-k)*a185951(n, k));
%Y A381378 Cf. A364980, A381376, A381382, A381384.
%Y A381378 Cf. A185951.
%K A381378 sign
%O A381378 0,3
%A A381378 _Seiichi Manyama_, Feb 22 2025