OFFSET
0,4
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows n = 0..150, flattened.)
Robert S. Maier, Sheffer Polynomials and the s-ordering of Exponential Boson Operators, arXiv:2508.13094 [quant-ph], 2025. See p. 27.
FORMULA
Number triangle T(n,k)=C(n,(n+k)/2)(-1)^((n+k)/2)(1+(-1)^(n+k))/2.
abs(T(n,k)) = A108044(n,k).
EXAMPLE
Triangle begins
1;
0, -1;
-2, 0, 1;
0, 3, 0, -1;
6, 0, -4, 0, 1;
0, -10, 0, 5, 0, -1;
-20, 0, 15, 0, -6, 0, 1;
0, 35, 0, -21, 0, 7, 0, -1;
70, 0, -56, 0, 28, 0, -8, 0, 1;
0, -126, 0, 84, 0, -36, 0, 9, 0, -1;
-252, 0, 210, 0, -120, 0, 45, 0, -10, 0, 1;
MATHEMATICA
T[n_, k_] := Binomial[n, (n + k)/2]*(-1)^((n + k)/2) (1 + (-1)^(n + k))/2; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Aug 22 2025 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Jun 17 2006
STATUS
approved