[seqfan] p-adic evaluat of k-central binom coeffs

[Richard Mathar]

The array

1,1,1,1,1,1,1,1,1,1,
2,6,20,70,252,924,3432,12870,48620,184756,
3,18,126,945,7371,58968,480168,3961386,33011550,277297020,
4,40,480,6240,84864,1188096,16972800,246105600,3609548800,53421322240,
5,75,1375,27500,577500,12512500,277062500,6233906250,141994531250,3265874218750,
6,126,3276,93366,2800980,86830380,2753763480,88808872230,2901089826180,95735964263940,

appears (implicitly) in Straub et al http://journals.impan.pl/cgi-bin/doi?aa140-1-2

and is defined as the expansion coefficients [x^n] of 1/(1-k^2*x)^(1/k)
k is the row index.
I suspect this is already in the OEIS but cannot find it...