OFFSET
0,2
COMMENTS
This triangle is the subject of the paper by Agarwal (1990).
LINKS
Ashok Agarwal, On a new kind of numbers, Fibonacci Quarterly, Vol. 28, No. 3 (1990), pp. 194-199.
R. K. Raina and H. M. Srivastava, A class of numbers associated with the Lucas numbers, Mathematical and Computer Modelling, Vol. 25, No. 7 (1997), pp. 15-22.
FORMULA
Sum_{k=0..n} T(n, k) = 1.
T(n + 1, k) = -(2n + 3)*(2n + 2)/((n - k + 1)*(n + k + 2)) * T(n, k).
MATHEMATICA
T[n_, k_] := (-1)^(n - k) * Binomial[2 n + 1, n - k] * LucasL[2 k + 1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten
PROG
(PARI) L(n) = fibonacci(n+1) + fibonacci(n-1); \\ A000032
T(n, k) = (-1)^(n - k) * binomial(2*n + 1, n - k) * L(2*k + 1); \\ Michel Marcus, Oct 21 2019
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Amiram Eldar, Oct 20 2019
STATUS
approved