A109962 - OEIS

%I #8 Jul 07 2020 07:56:55

%S 1,-1,1,4,-5,1,-22,30,-9,1,140,-200,72,-13,1,-969,1425,-570,130,-17,1,

%T 7084,-10626,4554,-1196,204,-21,1,-53820,81900,-36855,10647,-2142,294,

%U -25,1,420732,-647280,302064,-93496,21080,-3472,400,-29,1,-3362260,5217300,-2504304,816816,-200277,37485,-5250,522

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

%C 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.

%H Paul Drube, <a href="https://arxiv.org/abs/2007.01892">Generalized Path Pairs and Fuss-Catalan Triangles</a>, arXiv:2007.01892 [math.CO], 2020. See Figure 4 p. 8 (up to signs).

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

%e Rows begin

%e 1;

%e -1,1;

%e 4,-5,1;

%e -22,30,-9,1;

%e 140,-200,72,-13,1;

%e -969,1425,-570,130,-17,1;

%K easy,sign,tabl

%O 0,4

%A _Paul Barry_, Jul 06 2005