%I A003583
%S A003583 1,5,26,130,628,2954,13612,61716,276200,1223002,5367676,
%T A003583 23383100,101215576,435712580,1866667448,7963424104,33846062544,
%U A003583 143373104378,605518549660,2550438016812,10716162617336
%N A003583 (n+2)*2^(2*n-1)-(n/2)*binomial(2*n,n).
%D A003583 M. Hirschhorn, Calkin's binomial identity, Discr. Math., 159 (1996), 
               273-278.
%D A003583 Jun Wang and Zhizheng Zhang, On extensions of Calkin's binomial identities, 
               Discrete Math., 274 (2004), 331-342.
%F A003583 Main diagonal of correlation matrix of A055248. a(n)=sum{k=0..n, (sum{m=k..n, 
               binomial(n, m)})^2 } - Paul Barry (pbarry(AT)wit.ie), Jun 05 2003
%F A003583 Let S2 := (n, t)->add( k^t * (add( binomial(n, j), j=0..k))^2, k=0..n); 
               a(n) = S2(n, 0).
%Y A003583 Sequence in context: A047669 A002316 A005499 this_sequence A033115 A033123 
               A047770
%Y A003583 Adjacent sequences: A003580 A003581 A003582 this_sequence A003584 A003585 
               A003586
%K A003583 nonn
%O A003583 0,2
%A A003583 N. J. A. Sloane (njas(AT)research.att.com).