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 A104505 #21 Mar 27 2019 10:20:35
%S A104505 1,1,-1,-1,-2,1,-5,0,3,-1,-5,8,2,-4,1,11,15,-10,-5,5,-1,41,-6,-30,10,
%T A104505 9,-6,1,29,-77,-14,49,-7,-14,7,-1,-125,-120,112,56,-70,0,20,-8,1,-365,
%U A104505 117,288,-126,-126,90,12,-27,9,-1,-131,770,45,-540,90,228,-105,-30,35,-10,1,1409,946,-1265,-495,858,33,-363,110,55,-44
%N A104505 Triangle, read by rows, equal to the right-hand side of the triangle A084610, with row n listing the coefficients of (1+x-x^2)^n: T(n,k) = [x^(n+k)] (1+x-x^2)^n, for n>=k>=0.
%C A104505 Matrix inverse is triangle A104509 and is related to Fibonacci numbers. Column 0 equals A098331, with g.f.: 1/sqrt(1-2*x+5*x^2). Column 1 equals A104506, with g.f.: ((1-x)/sqrt(1-2*x+5*x^2)-1)/(2*x). Row sums equal A104507. Absolute row sums equal A104508.
%C A104505 Array (1/sqrt(1-2x+5x^2), (1-x-sqrt(1-2x+5x^2))/(2x)), in Riordan array notation. Product of A120616 by A007318. - _Paul Barry_, Jun 17 2006
%H A104505 P. Peart and W.-J. Woan, <a href="http://dx.doi.org/10.1016/S0166-218X(99)00166-3">A divisibility property for a subgroup of Riordan matrices</a>, Discrete Applied Mathematics, Vol. 98, Issue 3, Jan 2000, 255-263.
%F A104505 T(n, 0) = A098331(n). T(n, 1) = n*A007440(n) (n>0).
%F A104505 Column k has e.g.f. exp(x)*Bessel_I(k,2*sqrt(-1)x)*(sqrt(-1))^k. - _Paul Barry_, Jun 17 2006
%F A104505 From _Peter Bala_, Jun 29 2015: (Start)
%F A104505 Matrix factorization in the Riordan group: ( 1/(1 - x), x/(1 - x) ) * ( 1/sqrt(1 + 4*x^2), (1 - sqrt(1 + 4*x^2))/(2*x) ) = A007318 * signed version of A108044.
%F A104505 Riordan array has the form ( x*h'(x)/h(x), h(x) ) with h(x) = (1 - x - sqrt(1 - 2*x + 5*x^2))/(2*x) and so belongs to the hitting time subgroup H of the Riordan group (see Peart and Woan).
%F A104505 T(n,k) = [x^(n-k)] f(x)^n with f(x) = x^2 + x - 1. In general the (n,k)th entry of the hitting time array ( x*h'(x)/h(x), h(x) ) has the form [x^(n-k)] f(x)^n, where f(x) = x/( series reversion of h(x) ). (End)
%e A104505 Rows begin:
%e A104505 1;
%e A104505 1,-1;
%e A104505 -1,-2,1;
%e A104505 -5,0,3,-1;
%e A104505 -5,8,2,-4,1;
%e A104505 11,15,-10,-5,5,-1;
%e A104505 41,-6,-30,10,9,-6,1;
%e A104505 29,-77,-14,49,-7,-14,7,-1;
%e A104505 -125,-120,112,56,-70,0,20,-8,1;
%e A104505 -365,117,288,-126,-126,90,12,-27,9,-1;
%e A104505 -131,770,45,-540,90,228,-105,-30,35,-10,1; ...
%t A104505 T[n_, k_] := Coefficient[(1 + x - x^2)^n, x, n + k];
%t A104505 Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Mar 27 2019 *)
%o A104505 (PARI) T(n,k)=if(n<k || k<0,0,polcoeff((1+x-x^2)^n,n+k,x))
%Y A104505 Cf. A104509, A098331, A007440, A104506, A104507, A104508, A108044.
%K A104505 sign,tabl
%O A104505 0,5
%A A104505 _Paul D. Hanna_, Mar 11 2005