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 A386558 #19 Jul 26 2025 09:31:18 %S A386558 1,1,0,1,1,0,1,2,2,0,1,3,7,5,0,1,4,15,30,14,0,1,5,26,91,143,42,0,1,6, %T A386558 40,204,612,728,132,0,1,7,57,385,1771,4389,3876,429,0,1,8,77,650,4095, %U A386558 16380,32890,21318,1430,0,1,9,100,1015,8184,46376,158224,254475,120175,4862,0 %N A386558 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals: A(n,k) = binomial((k+1)*n+k-1,n)/(n+1). %H A386558 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fuss-Catalan_number">Fuss-Catalan number</a> %F A386558 For k > 0, A(n,k) = r * binomial(n*p+r,n)/(n*p+r), the Fuss-Catalan number with p=k+1 and r=k. %F A386558 G.f. of column k: (1/x) Series_Reverion( x*(1-x)^k ). %e A386558 Square array begins: %e A386558 1, 1, 1, 1, 1, 1, 1, ... %e A386558 0, 1, 2, 3, 4, 5, 6, ... %e A386558 0, 2, 7, 15, 26, 40, 57, ... %e A386558 0, 5, 30, 91, 204, 385, 650, ... %e A386558 0, 14, 143, 612, 1771, 4095, 8184, ... %e A386558 0, 42, 728, 4389, 16380, 46376, 109668, ... %e A386558 0, 132, 3876, 32890, 158224, 548340, 1533939, ... %o A386558 (PARI) a(n, k) = binomial((k+1)*n+k-1, n)/(n+1); %Y A386558 Columns k=0..10 give A000007, A000108, A006013, A006632, A118971, A130564(n+1), A130565(n+1), A234466, A234513, A234573, A235340. %Y A386558 Main diagonal gives A177784(n+1). %Y A386558 Cf. A162382. %K A386558 nonn,tabl,easy %O A386558 0,8 %A A386558 _Seiichi Manyama_, Jul 26 2025