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 A381282 #10 Feb 19 2025 03:38:20
%S A381282 1,1,2,-6,-72,-520,-1200,24752,516992,5106816,5287680,-998945024,
%T A381282 -23719719936,-272471972864,1326261594112,149170761246720,
%U A381282 3843177252618240,42752553478356992,-863092250325614592,-59317347865870139392,-1577115871098630307840,-13173264127625587851264
%N A381282 Expansion of e.g.f. 1/(1 - x * cos(2*x)).
%C A381282 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381282 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-4)^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%F A381282 a(n) = Sum_{k=0..n} k! * (2*i)^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381282 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381282 a(n) = sum(k=0, n, k!*(2*I)^(n-k)*a185951(n, k));
%Y A381282 Cf. A352252, A381283.
%Y A381282 Cf. A185951.
%K A381282 sign
%O A381282 0,3
%A A381282 _Seiichi Manyama_, Feb 18 2025