A109576 E.g.f.: x/(1+3x-4x^3)=x/[1-T(3,x)], where T(3,x) is a Chebyshev polynomial.

0, 1, -6, 54, -552, 6840, -97200, 1577520, -28667520, 578067840, -12798777600, 308836281600, -8065907942400, 226719600307200, -6824229456844800, 219010610827008000, -7465397891567616000, 269363867734241280000, -10256545055212904448000

Offset

0,3

Comments

"Bernoulli numbers" for x/[1-T(3,x)].

Links

Table of n, a(n) for n=0..18.

Formula

D-finite with recurrence a(n) +(n+4)*a(n-1) -2*n*(n-1)*a(n-2) -4*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Aug 20 2021

Maple

G:=x/(1+3*x-4*x^3): Gser:=series(G, x=0, 23): 0, seq(n!*coeff(Gser, x^n), n=1..20); # yields the signed sequence

Mathematica

g[x_] = x/(-1 + ChebyshevT[3, x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 50}]; b = a[0]

Crossrefs

Sequence in context: A098658 A357164 A357225 * A365843 A366014 A241843

Adjacent sequences: A109573 A109574 A109575 * A109577 A109578 A109579

Keyword

sign

Author

Roger L. Bagula, Jun 28 2005

Status

approved