This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A248332 #23 Nov 11 2024 03:56:39 %S A248332 1,8,56,288,224,3360,13056,5376,8960,206080,652800,182784,161280, %T A248332 412160,12776960,34467840,7311360,4386816,5935104,20443136,797282304, %U A248332 1884241920,321699840,146227200,134529024,245317632,1063043072,49963024384,105517547520,15073935360,5514854400,3843686400 %N A248332 Square array read by antidiagonals downwards: super Patalan numbers of order 8. %C A248332 Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 8, A025753. %H A248332 Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014. %H A248332 Thomas M. Richardson, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Richardson/rich2.html">The Super Patalan Numbers</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.3. %F A248332 T(0,0)=1, T(n,k) = T(n-1,k)*(64*n-8)/(n+k), T(n,k) = T(n,k-1)*(64*k-56)/(n+k). %F A248332 G.f.: (x/(1-64*x)^(7/8)+y/(1-64*y)^(1/8))/(x+y-64*x*y). %F A248332 T(n,k) = (-1)^k*64^(n+k)*binomial(n-1/8,n+k). %e A248332 T(0..4,0..4) is %e A248332 1 8 288 13056 652800 %e A248332 56 224 5376 182784 7311360 %e A248332 3360 8960 161280 4386816 146227200 %e A248332 206080 412160 5935104 134529024 3843686400 %e A248332 12776960 20443136 245317632 4766171136 119154278400 %o A248332 (PARI) matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*64^(n+k)*binomial(n-1/8,n+k)) \\ _Michel Marcus_, Oct 09 2014 %Y A248332 Cf. A068555, A025753, A034977 (first row), A216704 (first column), A248324, A248325, A248326, A248328, A248329. %K A248332 nonn,tabl,easy %O A248332 0,2 %A A248332 _Tom Richardson_, Oct 04 2014