A352640 - 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