A352639 - OEIS

%I #14 Mar 26 2022 13:41:56

%S 1,2,4,6,0,-46,-192,-266,1792,14114,34816,-171930,-2027520,-6522382,

%T 34750464,496296022,1748500480,-12731696062,-186550845440,

%U -617309234490,7292215885824,99199654760978,248883934396416,-5836506132182090,-69729013345550336

%N Expansion of e.g.f. exp(2*sin(x)).

%F a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1).

%t With[{m = 24}, Range[0, m]! * CoefficientList[Series[Exp[2*Sin[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*sin(x))))

%o (PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (-1)^k*binomial(n-1, 2*k)*a(n-2*k-1)));

%Y Cf. A002017, A352640.

%Y Cf. A007289, A352279, A352642.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 25 2022