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 A381209 #12 Feb 17 2025 08:18:26
%S A381209 1,3,12,51,216,735,0,-39081,-575232,-6047973,-48314880,-189159333,
%T A381209 3046957056,99745485879,1789140627456,23433663134655,185580069027840,
%U A381209 -1250544374605389,-94781673979379712,-2543434372808424957,-47763303489939701760,-586864592847636893937
%N A381209 Expansion of e.g.f. 1/(1 - x*cos(x))^3.
%C A381209 As stated in the comment of A185951, A185951(n,0) = 0^n.
%F A381209 a(n) = 1/2 * Sum_{k=0..n} (k+2)! * i^(n-k) * A185951(n,k), where i is the imaginary unit.
%o A381209 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A381209 a(n) = sum(k=0, n, (k+2)!*I^(n-k)*a185951(n, k))/2;
%Y A381209 Cf. A377530, A381207, A381210, A381211.
%Y A381209 Cf. A352252, A381208.
%Y A381209 Cf. A185951.
%K A381209 sign
%O A381209 0,2
%A A381209 _Seiichi Manyama_, Feb 17 2025