Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Mar 26 2022 13:41:52
%S 1,3,9,24,45,-24,-747,-3864,-7623,48576,548001,2175360,-5269275,
%T -133496448,-785549331,789324288,52523738865,398157422592,
%U -157735851975,-31426593116160,-278010988509411,108354846277632,27060485795905221,257882404940021760
%N Expansion of e.g.f. exp(3*sin(x)).
%F a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1).
%t With[{m = 23}, Range[0, m]! * CoefficientList[Series[Exp[3*Sin[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*sin(x))))
%o (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y Cf. A002017, A352639.
%Y Cf. A352280, A352638.
%K sign
%O 0,2
%A _Seiichi Manyama_, Mar 25 2022