OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..949
FORMULA
G.f.: A(x) = 1 + (x/(1+x^2))*A(x/(1+x^2)).
EXAMPLE
Eigensequence for the number triangle
1;
1, 0;
0, 1, 0;
-1, 0, 1, 0;
0, -2, 0, 1, 0;
1, 0, -3, 0, 1, 0;
0, 3, 0, -4, 0, 1, 0;
-1, 0, 6, 0, -5, 0, 1, 0;
0, -4, 0, 10, 0, -6, 0, 1, 0;
1, 0, -10, 0, 15, 0, -7, 0, 1, 0;
0, 5, 0, -20, 0, 21, 0, -8, 0, 1, 0;
(augmented version of Riordan array (1/(1+x^2), x/(1+x^2)).
MATHEMATICA
a[n_] := If[n == 0, 1, Sum[Binomial[n - k - 1, k]*(-1)^k*a[n - 2*k - 1], {k, 0, Floor[(n - 1)/2]}]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 07 2018 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Feb 01 2010
EXTENSIONS
Name corrected by G. C. Greubel, Oct 07 2018
Terms a(27) and beyond from Seiichi Manyama, Feb 25 2023
STATUS
approved