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 A248326 #29 Nov 11 2024 03:56:58 %S A248326 1,5,20,75,50,450,1375,500,750,10500,27500,6875,5625,13125,249375, %T A248326 577500,110000,61875,78750,249375,5985000,12512500,1925000,825000, %U A248326 721875,1246875,4987500,144637500,277062500,35750000,12375000,8250000,9796875,21375000,103312500,3512625000,6233906250,692656250 %N A248326 Square array read by downward antidiagonals: super Patalan numbers of order 5. %C A248326 Generalization of super Catalan numbers of Gessel, A068555, based on Patalan numbers of order 5, A025750. %H A248326 Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014. %H A248326 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 A248326 T(0,0)=1, T(n,k) = T(n-1,k)*(25*n-5)/(n+k), T(n,k) = T(n,k-1)*(25*k-20)/(n+k). %F A248326 G.f.: (x/(1-25*x)^(4/5)+y/(1-25*y)^(1/5))/(x+y-25*x*y). %F A248326 T(n,k) = (-1)^k*25^(n+k)*binomial(n-1/5,n+k). %e A248326 T(0..4,0..4) is %e A248326 1 5 75 1375 27500 %e A248326 20 50 500 6875 110000 %e A248326 450 750 5625 61875 825000 %e A248326 10500 13125 78750 721875 8250000 %e A248326 249375 249375 1246875 9796875 97968750 %o A248326 (PARI) matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*25^(n+k)*binomial(n-1/5,n+k)) \\ _Michel Marcus_, Oct 09 2014 %Y A248326 Cf. A068555, A025750, A034688 (first row), A049382 (first column), A248324, A248325, A248328, A248329, A248332. %K A248326 nonn,easy,tabl %O A248326 0,2 %A A248326 _Tom Richardson_, Oct 04 2014