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 A101516 #5 Mar 30 2012 18:36:44
%S A101516 1,2,4,8,17,38,91,232,632,1824,5571,17892,60355,212898,784416,3008480,
%T A101516 11997341,49612426,212536067,941213428,4305049140,20302469824,
%U A101516 98641434683,493038167880,2533414749409,13366134856170,72361098996208
%N A101516 Antidiagonal sums of symmetric square array A101515 and also equals the binomial transform of a sequence formed from terms of A101514 repeated twice.
%C A101516 A101514 equals the main diagonal of A101515 shift one place right and also A101514 shifts one place left under the square binomial transform (A008459): A101514(n+1) = Sum_{k=0..n-1} C(n-1,k)^2*A101514(k).
%F A101516 G.f.: A(x) = G101514(x^2/(1-x)^2)/(1-x)^2, where G101514(x)= g.f. of A101514. a(n) = Sum_{k=0..n} C(n, k)*A101514([k/2]).
%e A101516 Given A101514 = [1,1,2,7,35,236,2037,21695,277966,4198635,...],
%e A101516 the binomial transform of A101514 terms repeated twice returns this sequence:
%e A101516 BINOMIAL[1,1,1,1,2,2,7,7,35,35,...] = [1,2,4,8,17,38,91,232,632,1824,...].
%o A101516 (PARI) {a(n)=sum(k=0,n,binomial(n,k)* if(k\2==0,1,sum(j=0,k\2-1,binomial(k\2-1,j)^2* sum(i=0,2*j,(-1)^(2*j-i)*binomial(2*j,i)*a(i)))))}
%Y A101516 Cf. A101514, A101515.
%K A101516 nonn
%O A101516 0,2
%A A101516 _Paul D. Hanna_, Dec 06 2004