A061896 Triangle of coefficients of Lucas polynomials.

2, 1, 0, 1, 2, 0, 1, 3, 0, 0, 1, 4, 2, 0, 0, 1, 5, 5, 0, 0, 0, 1, 6, 9, 2, 0, 0, 0, 1, 7, 14, 7, 0, 0, 0, 0, 1, 8, 20, 16, 2, 0, 0, 0, 0, 1, 9, 27, 30, 9, 0, 0, 0, 0, 0, 1, 10, 35, 50, 25, 2, 0, 0, 0, 0, 0, 1, 11, 44, 77, 55, 11, 0, 0, 0, 0, 0, 0, 1, 12, 54, 112, 105, 36, 2, 0, 0, 0, 0, 0, 0, 1, 13

Offset: 0

Author

Henry Bottomley, May 14 2001

Keywords

• nonn
• tabl

Examples

			Triangle begins:
2,
1, 0.
1, 2, 0.
1, 3, 0, 0.
1, 4, 2, 0, 0.
1, 5, 5, 0, 0, 0.
1, 6, 9, 2, 0, 0, 0.
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Alternative version of A034807. With alternating signs, these are the coefficients of the recurrences in A061897.

Programs

Mathematica

a[0, 0] := 2; a[n_, 0] := 1; a[n_, n_] := 0; a[n_, k_] := Binomial[n - k, k]*n/(n - k); Table[a[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Oct 15 2017 *)

Formula

a(n, k) = C(n-k, k)*n/(n-k).

a(n, k) = C(n-k, k) + C(n-k-1, k-1).

a(n, k) = a(n-1, k) + a(n-2, k-1) with a(n, 0)=1 if n>0 and a(0, 0)=2.