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 A248329 #24 Nov 11 2024 03:56:48 %S A248329 1,7,42,196,147,1911,6860,2744,4459,89180,264110,72030,62426,156065, %T A248329 4213755,10722866,2218524,1310946,1747928,5899257,200574738,450360372, %U A248329 75060062,33647614,30588740,55059732,234003861,9594158301,19365495996,2702162232,975780806,672952280,825895980,1872030888 %N A248329 Square array read by antidiagonals downwards: super Patalan numbers of order 7. %C A248329 Generalization of super Catalan numbers, A068555, based on Patalan numbers of order 7, A025752. %H A248329 Thomas M. Richardson, <a href="http://arxiv.org/abs/1410.5880">The Super Patalan Numbers</a>, arXiv:1410.5880 [math.CO], 2014. %H A248329 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 A248329 T(0,0)=1, T(n,k) = T(n-1,k)*(49*n-7)/(n+k), T(n,k) = T(n,k-1)*(49*k-42)/(n+k). %F A248329 G.f.: (x/(1-49*x)^(6/7)+y/(1-49*y)^(1/7))/(x+y-49*x*y). %F A248329 T(n,k) = (-1)^k*49^(n+k)*binomial(n-1/7,n+k). %e A248329 T(0..4,0..4) is %e A248329 1 7 196 6860 264110 %e A248329 42 147 2744 72030 2218524 %e A248329 1911 4459 62426 1310946 33647614 %e A248329 89180 156065 1747928 30588740 672952280 %e A248329 4213755 5899257 55059732 825895980 15898497615 %o A248329 (PARI) matrix(5, 5, nn, kk, n=nn-1;k=kk-1;(-1)^k*49^(n+k)*binomial(n-1/7,n+k)) \\ _Michel Marcus_, Oct 09 2014 %Y A248329 Cf. A068555, A025752, A034835 (first row), A216703 (first column), A248324, A248325, A248326, A248328, A248332. %K A248329 nonn,tabl,easy %O A248329 0,2 %A A248329 _Tom Richardson_, Oct 04 2014