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A061896 Triangle of coefficients of Lucas polynomials. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
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
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, May 14 2001
STATUS
approved

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Last modified February 21 10:32 EST 2024. Contains 370228 sequences. (Running on oeis4.)