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 A112973 #16 Apr 21 2015 04:52:15
%S A112973 1,1,1,2,4,1,3,12,7,1,5,31,31,10,1,8,73,110,59,13,1,13,162,340,267,96,
%T A112973 16,1,21,344,956,1022,529,142,19,1,34,707,2507,3479,2416,923,197,22,1,
%U A112973 55,1416,6231,10850,9657,4900,1476,261,25,1,89,2778,14840,31606,34905
%N A112973 Riordan array (1/(1-x-x^2), x(1+x)/(1-x-x^2)^2).
%C A112973 Row sums are A091702. Diagonal sums are A052960. First column is A000045(n+1).
%C A112973 Second column is A129707. - _Ralf Stephan_, Dec 31 2013
%F A112973 T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) - 2*T(n-3,k) - T(n-4,k), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 4, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Jan 21 2014
%F A112973 G.f.: (x^2+x-1)/((x^2+x)*y-x^4-2*x^3+x^2+2*x-1). - _Vladimir Kruchinin_, Apr 21 2015
%F A112973 T(n,k) = Sum_{m=floor(n/2)..n} C(m,n-m)*C(m+k,2*k). - _Vladimir Kruchinin_, Apr 21 2015
%e A112973 Rows begin
%e A112973 1;
%e A112973 1,1;
%e A112973 2,4,1;
%e A112973 3,12,7,1;
%e A112973 5,31,31,10,1;
%e A112973 8,73,110,59,13,1;
%o A112973 (Maxima) T(n,k):=sum(binomial(m,n-m)*binomial(m+k,2*k),m,floor(n/2),n); /* _Vladimir Kruchinin_, Apr 21 2015 */
%K A112973 easy,nonn,tabl
%O A112973 0,4
%A A112973 _Paul Barry_, Oct 07 2005
%E A112973 Definition corrected by _Ralf Stephan_, Dec 31 2013