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 A112899 #14 Jan 21 2025 02:28:04
%S A112899 1,0,2,0,1,5,0,0,4,12,0,0,1,14,29,0,0,0,6,44,70,0,0,0,1,27,131,169,0,
%T A112899 0,0,0,8,104,376,408,0,0,0,0,1,44,366,1052,985,0,0,0,0,0,10,200,1212,
%U A112899 2888,2378,0,0,0,0,0,1,65,810,3842,7813,5741,0,0,0,0,0,0,12,340,3032,11784
%N A112899 A skew Pell-Pascal triangle.
%C A112899 Main diagonal is A000129. Row sums are A002605. Column sums are A006190(n+1).
%C A112899 A skewed version of the Riordan array (1/(1-2x-x^2), x/(1-2x-x^2)), see A054456. - _Philippe Deléham_, Nov 21 2007
%C A112899 Triangle, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,...] DELTA [2,1/2,-1/2,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Jan 30 2010
%F A112899 G.f.: 1/(1-2*x*y*(1+x/2)-x^2*y^2).
%F A112899 T(n, k) = Sum_{j=0..floor((2*k-n)/2)} C(k-j, n-k)*C(2*k-n-j, j)*2^(2*k-2*j-n). [corrected by _Jason Yuen_, Jan 21 2025]
%F A112899 T(n, k) = 2*T(n-1, k-1) + T(n-2, k-1) + T(n-2, k-2).
%e A112899 Rows begin:
%e A112899 1;
%e A112899 0, 2;
%e A112899 0, 1, 5;
%e A112899 0, 0, 4, 12;
%e A112899 0, 0, 1, 14, 29;
%e A112899 0, 0, 0, 6, 44, 70;
%e A112899 0, 0, 0, 1, 27, 131, 169;
%e A112899 0, 0, 0, 0, 8, 104, 376, 408;
%Y A112899 Cf. A111006, A112906. - _Philippe Deléham_, Jan 30 2010
%K A112899 easy,nonn,tabl
%O A112899 0,3
%A A112899 _Paul Barry_, Oct 05 2005