A381283 - OEIS

%I #11 Feb 19 2025 03:38:33

%S 1,1,2,-21,-192,-1095,7200,243747,3088512,1360881,-874437120,

%T -21701765349,-186175604736,5870711879721,292185085151232,

%U 5507319584787795,-38951106749890560,-6402114772676575263,-212680600451474522112,-1602903494245708491957,197042528380347210792960

%N Expansion of e.g.f. 1/(1 - x * cos(3*x)).

%C As stated in the comment of A185951, A185951(n,0) = 0^n.

%F 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 a(n) = Sum_{k=0..n} k! * (3*i)^(n-k) * A185951(n,k), where i is the imaginary unit.

%o (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));

%o a(n) = sum(k=0, n, k!*(3*I)^(n-k)*a185951(n, k));

%Y Cf. A352252, A381282.

%Y Cf. A185951.

%K sign,new

%O 0,3

%A _Seiichi Manyama_, Feb 18 2025