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 A381283 #11 Feb 19 2025 03:38:33
%S A381283 1,1,2,-21,-192,-1095,7200,243747,3088512,1360881,-874437120,
%T A381283 -21701765349,-186175604736,5870711879721,292185085151232,
%U A381283 5507319584787795,-38951106749890560,-6402114772676575263,-212680600451474522112,-1602903494245708491957,197042528380347210792960
%N A381283 Expansion of e.g.f. 1/(1 - x * cos(3*x)).
%C A381283 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381283 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%F A381283 a(n) = Sum_{k=0..n} k! * (3*i)^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381283 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381283 a(n) = sum(k=0, n, k!*(3*I)^(n-k)*a185951(n, k));
%Y A381283 Cf. A352252, A381282.
%Y A381283 Cf. A185951.
%K A381283 sign
%O A381283 0,3
%A A381283 _Seiichi Manyama_, Feb 18 2025