Search: id:A113413
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%I A113413
%S A113413 1,2,1,2,4,1,2,8,6,1,2,12,18,8,1,2,16,38,32,10,1,2,20,66,88,50,12,1,2,
%T A113413 24,102,192,170,72,14,1,2,28,146,360,450,292,98,16,1,2,32,198,608,1002,
%U A113413 912,462,128,18,1,2,36,258,952,1970,2364,1666,688,162,20,1,2,40,326
%N A113413 A Riordan array of coordination sequences.
%C A113413 Columns include A040000,A008574,A005899,A008412,A008413,A008414. Row 
               sums are A078057(n)=A001333(n+1). Diagonal sums are A001590(n+3). 
               Reverse of A035607. Signed version is A080246. Inverse is A080245.
%C A113413 For another version see A122542. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 15 2006
%F A113413 Riordan array ((1+x)/(1-x), x(1+x)/(1-x)); T(n, k)=sum{i=0..n-k, C(k+1, 
               i)C(n-i, k)}; T(n, k)=sum{j=0..n-k, C(k+j, j)C(k+1, n-k-j)}; T(n, 
               k)=D(n, k)+D(n-1, k) where D(n, k)=sum{j=0..n-k, C(n-k, j)C(k, j)2^j}=A008288(n, 
               k); T(n, k)=T(n-1, k)+T(n-1, k-1)+T(n-2, k-1);
%F A113413 T(n, k)=sum{j=0..n, C(floor((n+j)/2), k)C(k, floor((n-j)/2))}; - Paul 
               Barry (pbarry(AT)wit.ie), Nov 13 2005
%e A113413 Triangle begins
%e A113413 1;
%e A113413 2, 1;
%e A113413 2, 4, 1;
%e A113413 2, 8, 6, 1;
%e A113413 2, 12, 18, 8, 1;
%e A113413 2, 16, 38, 32, 10, 1;
%e A113413 2, 20, 66, 88, 50, 12, 1;
%Y A113413 Sequence in context: A114791 A129994 A080246 this_sequence A125694 A136678 
               A110162
%Y A113413 Adjacent sequences: A113410 A113411 A113412 this_sequence A113414 A113415 
               A113416
%K A113413 easy,nonn,tabl
%O A113413 0,2
%A A113413 Paul Barry (pbarry(AT)wit.ie), Oct 29 2005

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