A352646 Expansion of e.g.f. 1/(1 - 2 * x * cos(x)).

1, 2, 8, 42, 288, 2410, 24000, 277186, 3648512, 53936082, 885150720, 15970846298, 314273439744, 6698574264122, 153746319720448, 3780677636321010, 99163499845386240, 2763481838977368994, 81542013760903053312, 2539717324111483027594

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..415

Formula

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

a(n) ~ n! / ((1 - r * sqrt(4*r^2 - 1)) * r^n), where r = A196603 = 0.6100312844641759753709630735134103246737209791121692378637516075328... is the root of the equation 2*r*cos(r) = 1. - Vaclav Kotesovec, Mar 27 2022

Mathematica

With[{m = 19}, Range[0, m]! * CoefficientList[Series[1/(1 - 2*x*Cos[x]), {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x*cos(x))))
(PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));

Crossrefs

Cf. A352252, A352647.

Cf. A352642, A352648.

Sequence in context: A078592 A225108 A052646 * A320343 A002856 A093461

Adjacent sequences: A352643 A352644 A352645 * A352647 A352648 A352649

Keyword

nonn

Author

Seiichi Manyama, Mar 25 2022

Status

approved