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 A160905 #10 May 09 2025 07:11:07
%S A160905 1,1,1,4,2,1,9,8,3,1,29,22,13,4,1,82,72,42,19,5,1,255,218,146,70,26,6,
%T A160905 1,773,691,476,261,107,34,7,1,2410,2158,1574,914,428,154,43,8,1,7499,
%U A160905 6833,5122,3177,1603,659,212,53,9,1,23575,21612,16706,10816,5867,2628,967
%N A160905 Right hand side of Pascal rhombus A059317.
%C A160905 Riordan array (1/sqrt((1+x-x^2)*(1-3*x-x^2)), (1-x-x^2-sqrt((1+x-x^2)*(1-3*x-x^2)))/(2*x)). Can be factored as
%C A160905 (1/(1-x-x^2), x/(1-x-x^2))*(1/sqrt(1-4x^2),xc(x^2)) = (1/(1-x^2),x/(1-x^2))*(1/(1-x),x/(1-x))*(1/sqrt(1-4x^2),xc(x^2))
%C A160905 and (1/(1-x^2),x/(1-x^2))*(1/sqrt(1-2x-3x^2),(1-x-sqrt(1-2x-3x^2))/(2x)).
%C A160905 Here, c(x) is the g.f. of the Catalan numbers A000108.
%C A160905 A160905 = A037027*A108044 = abs(A049310)*A007318*A108044 = abs(A049310)*A094531.
%F A160905 Number triangle T(n,k) = Sum_{i=0..n} (Sum_{j=0..n} C((n+j)/2,j)*C(j,i)*(1+(-1)^(n-j))/2)*C(i,(i-k)/2)*(1+(-1)^(i-k))/2;
%F A160905 T(n,k) = Sum_{j=0..n} C((n+j)/2,j)*((1+(-1)^(n-j))/2)*Sum_{i=0..j} C(j,i)*C(i,j-k-i).
%e A160905 Triangle begins:
%e A160905 1;
%e A160905 1, 1;
%e A160905 4, 2, 1;
%e A160905 9, 8, 3, 1;
%e A160905 29, 22, 13, 4, 1;
%e A160905 82, 72, 42, 19, 5, 1;
%e A160905 255, 218, 146, 70, 26, 6, 1;
%e A160905 ...
%Y A160905 Left column gives A059345.
%Y A160905 Cf. A059317.
%K A160905 easy,nonn,tabl
%O A160905 0,4
%A A160905 _Paul Barry_, May 29 2009