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 A202193 #25 Feb 17 2025 03:17:27
%S A202193 1,1,1,2,2,1,4,5,3,1,8,12,9,4,1,15,28,25,14,5,1,29,62,66,44,20,6,1,56,
%T A202193 136,165,129,70,27,7,1,108,294,401,356,225,104,35,8,1,208,628,951,944,
%U A202193 676,363,147,44,9,1,401,1328,2211,2424,1935,1176,553,200,54,10,1
%N A202193 Triangle read by rows: T(n,m) = coefficient of x^n in expansion of (x/(1 - x - x^2 - x^3 - x^4))^m.
%C A202193 From _Philippe Deléham_, Feb 16 2014: (Start)
%C A202193 As a Riordan array, this is (1/(1 - x - x^2 - x^3 - x^4), x/(1 - x - x^2 - x^3 - x^4)).
%C A202193 T(n,0) = A000078(n+3); T(n+1,1) = A118898(n+4).
%C A202193 Row sums are A103142(n).
%C A202193 Diagonal sums are A077926(n)*(-1)^n.
%C A202193 Tetranacci convolution triangle. (End)
%F A202193 T(n,m) = Sum_{k=1..n-m} (Sum_{i=0..floor((n-m-k)/4)} (-1)^i*binomial(k,k-i)*binomial(n-m-4*i-1,k-1))*binomial(k+m-1,m-1), n > m, T(n,n)=1.
%F A202193 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-3,k) + T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k < 0 or if k > n. - _Philippe Deléham_, Feb 16 2014
%F A202193 G.f. for column m: (x/(1 - x - x^2 - x^3 - x^4))^m. - _Jason Yuen_, Feb 17 2025
%e A202193 Triangle begins:
%e A202193 1;
%e A202193 1, 1;
%e A202193 2, 2, 1;
%e A202193 4, 5, 3, 1;
%e A202193 8, 12, 9, 4, 1;
%e A202193 15, 28, 25, 14, 5, 1;
%e A202193 29, 62, 66, 44, 20, 6, 1;
%o A202193 (Maxima)
%o A202193 T(n,m):=if n=m then 1 else sum(sum((-1)^i*binomial(k,k-i)*binomial(n-m-4*i-1,k-1),i,0,(n-m-k)/4)*binomial(k+m-1,m-1),k,1,n-m);
%Y A202193 Similar sequences : A037027 (Fibonacci convolution triangle), A104580 (tribonacci convolution triangle). - _Philippe Deléham_, Feb 16 2014
%K A202193 nonn,tabl
%O A202193 1,4
%A A202193 _Vladimir Kruchinin_, Dec 14 2011