A109962 - OEIS

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

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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 Barry, d-orthogonal polynomials, Fuss-Catalan matrices and lattice paths, arXiv:2505.16718 [math.CO], 2025. See p. 14.

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