A352640 Expansion of e.g.f. exp(3*sin(x)).

1, 3, 9, 24, 45, -24, -747, -3864, -7623, 48576, 548001, 2175360, -5269275, -133496448, -785549331, 789324288, 52523738865, 398157422592, -157735851975, -31426593116160, -278010988509411, 108354846277632, 27060485795905221, 257882404940021760

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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).

Mathematica

With[{m = 23}, Range[0, m]! * CoefficientList[Series[Exp[3*Sin[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*sin(x))))
(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)));

Crossrefs

Cf. A002017, A352639.

Cf. A352280, A352638.

Sequence in context: A338124 A024314 A120012 * A029530 A301740 A227018

Adjacent sequences: A352637 A352638 A352639 * A352641 A352642 A352643

Keyword

sign

Author

Seiichi Manyama, Mar 25 2022

Status

approved