Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Jul 07 2020 07:47:31
%S 1,-2,1,7,-5,1,-30,25,-8,1,143,-130,52,-11,1,-728,700,-320,88,-14,1,
%T 3876,-3876,1938,-627,133,-17,1,-21318,21945,-11704,4235,-1078,187,
%U -20,1,120175,-126500,70840,-27830,8050,-1700
%N Number triangle T(n,k)=(-1)^(n-k)*(3k+2)*C(3n+1, n-k)/(2n+k+2).
%C Inverse of number triangle A124819. Row sums are (-1)^n*A001764(n).
%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).
%e Triangle begins
%e 1,
%e -2, 1,
%e 7, -5, 1,
%e -30, 25, -8, 1,
%e 143, -130, 52, -11, 1,
%e -728, 700, -320, 88, -14, 1,
%e 3876, -3876, 1938, -627, 133, -17, 1
%Y Cf. A124019.
%K easy,sign,tabl
%O 0,2
%A _Paul Barry_, Nov 08 2006