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 A381286 #12 Feb 19 2025 03:39:09
%S A381286 1,1,2,-3,-48,-339,-1008,10737,237312,2362041,5432832,-318158523,
%T A381286 -7615254528,-87216236379,173049219072,33959321252217,851545449234432,
%U A381286 9561733579228401,-129701862228492288,-9445723672920941043,-239815723596207095808,-2109465061216228379619
%N A381286 Expansion of e.g.f. 1/(1 - sin(3*x) / 3).
%F A381286 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * binomial(n,2*k+1) * a(n-2*k-1).
%F A381286 a(n) = Sum_{k=0..n} k! * (3*i)^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381286 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381286 a(n) = sum(k=0, n, k!*(3*I)^(n-k)*a136630(n, k));
%Y A381286 Cf. A000111, A381285.
%Y A381286 Cf. A136630, A352638, A381278.
%K A381286 sign
%O A381286 0,3
%A A381286 _Seiichi Manyama_, Feb 18 2025