A144750 A098777 mod 9.

1, 8, 7, 2, 7, 5, 4, 5, 1, 8, 1, 2, 7, 2, 4, 5, 4, 8, 1, 8, 7, 2, 7, 5, 4, 5, 1, 8, 1, 2, 7, 2, 4, 5, 4, 8, 1, 8, 7, 2, 7, 5, 4, 5, 1, 8, 1, 2, 7, 2, 4, 5, 4, 8, 1, 8, 7, 2, 7, 5, 4, 5, 1, 8, 1, 2, 7, 2, 4, 5, 4, 8, 1, 8, 7, 2, 7, 5, 4, 5, 1, 8, 1, 2, 7, 2, 4, 5, 4, 8, 1, 8, 7, 2, 7, 5, 4, 5, 1, 8, 1

Offset: 0

Author

N. J. A. Sloane, Feb 08 2009

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• R. Bacher and P. Flajolet, Pseudo-factorials, Elliptic Functions and Continued Fractions, arXiv:0901.1379 [math.CA], 2009.

Programs

Maple

a:= proc(n) option remember; `if`(n=0,1,(-1)^n*add(binomial(n-1,k)*a(k)*a(n-1-k),k=0..n-1)) end: seq(modp(a(n),9), n=0..100); # Muniru A Asiru, Jul 29 2018

Mathematica

b[0] = 1;
b[n_] := b[n] = (-1)^n Sum[Binomial[n-1, k] b[k] b[n-k-1], {k, 0, n-1}];
a[n_] := Mod[b[n], 9]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 29 2018 *)

Formula

From Chai Wah Wu, Nov 30 2018: (Start)

a(n) = a(n-2) + a(n-3) - a(n-5) - a(n-6) + a(n-8) for n > 7 (conjectured).

G.f.: (-8*x^7 - 4*x^6 + 3*x^5 + 8*x^4 + 7*x^3 - 6*x^2 - 8*x - 1)/((x - 1)*(x + 1)*(x^6 - x^3 + 1)) (conjectured). (End)