A109962 Inverse of Riordan array (1/(1-x), x/(1-x)^4), A109960.

1, -1, 1, 4, -5, 1, -22, 30, -9, 1, 140, -200, 72, -13, 1, -969, 1425, -570, 130, -17, 1, 7084, -10626, 4554, -1196, 204, -21, 1, -53820, 81900, -36855, 10647, -2142, 294, -25, 1, 420732, -647280, 302064, -93496, 21080, -3472, 400, -29, 1, -3362260, 5217300, -2504304, 816816, -200277, 37485, -5250, 522

Offset

0,4

Comments

Riordan array (g,f) where f/(1-f)^4=x and g=1/(1-f). First column is (-1)^n*A002293(n). Diagonal sums are A109963.

Links

Table of n, a(n) for n=0..52.

Paul Drube, Generalized Path Pairs and Fuss-Catalan Triangles, arXiv:2007.01892 [math.CO], 2020. See Figure 4 p. 8 (up to signs).

Formula

Number triangle T(n, k)=(-1)^(n-k)*((4k+1)/(3n+k+1))*binomial(4n, n-k).

Example

Rows begin
1;
-1,1;
4,-5,1;
-22,30,-9,1;
140,-200,72,-13,1;
-969,1425,-570,130,-17,1;

Crossrefs

Sequence in context: A210590 A108446 A283263 * A102230 A147724 A110519

Adjacent sequences: A109959 A109960 A109961 * A109963 A109964 A109965

Keyword

easy,sign,tabl

Author

Paul Barry, Jul 06 2005

Status

approved