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

0,1

Links

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

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.

Example

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.

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 *)

Crossrefs

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

Sequence in context: A356733 A321100 A244422 * A366793 A069850 A141581

Adjacent sequences: A061893 A061894 A061895 * A061897 A061898 A061899

Keyword

nonn,tabl

Author

Henry Bottomley, May 14 2001

Status

approved