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A100218 Riordan array ((1-2x)/(1-x), (1-x)). 9
1, -1, 1, -1, -2, 1, -1, 0, -3, 1, -1, 0, 2, -4, 1, -1, 0, 0, 5, -5, 1, -1, 0, 0, -2, 9, -6, 1, -1, 0, 0, 0, -7, 14, -7, 1, -1, 0, 0, 0, 2, -16, 20, -8, 1, -1, 0, 0, 0, 0, 9, -30, 27, -9, 1, -1, 0, 0, 0, 0, -2, 25, -50, 35, -10, 1, -1, 0, 0, 0, 0, 0, -11, 55, -77, 44, -11, 1, -1, 0, 0, 0, 0, 0, 2, -36, 105, -112, 54 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

Number triangle T(n, k) = (-1)^(n-k)(binomial(k, n-k) + binomial(k-1, n-k-1)). - Paul Barry, Nov 09 2004

T(n,k) = T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k-1) + T(n-3,k-1), T(0,0)=1, T(1,0)=-1, T(1,1)=1, T(n,k)=0 if k < 0 or if k > n. - Philippe Deléham, Jan 09 2014

EXAMPLE

Rows begin {1}, {-1,1}, {-1,-2,1}, {-1,0,-3,1}, {-1,0,2,-4,1},...

MATHEMATICA

T[0, 0] := 1; T[1, 1] := 1; T[1, 0] := -1; T[n_, k_] := T[n, k] = If[k < 0 || k > n, 0, T[n - 1, k] + T[n - 1, k - 1] - 2*T[n - 2, k - 1] + T[n - 3, k - 1]]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Mar 13 2017 *)

CROSSREFS

Row sums are A100219. Matrix inverse of A100100.

Apart from signs, same as A098599. Very similar to triangle A111125.

Sequence in context: A175595 A175417 A136481 * A098599 A129334 A116399

Adjacent sequences:  A100215 A100216 A100217 * A100219 A100220 A100221

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Nov 08 2004

STATUS

approved

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Last modified March 25 08:15 EDT 2019. Contains 321469 sequences. (Running on oeis4.)