%I A102539
%S A102539 2,3,4,4,10,8,5,20,35,16,6,35,112,126,32,7,56,294,672,462,64,8,84,672,
%T A102539 2772,4224,1716,128,9,120,1386,9504,28314,27456,6435,256,10,165,2640,
%U A102539 28314,151008,306735,183040,24310,512,11,220,4719,75504,674817
%N A102539 Square array T(n,k) read by antidiagonals: Prod[1<=i<=j<=k, (n+i+j-1)/
               (i+j-1) ].
%C A102539 Number of semistandard Young tableaux with at most n columns and with 
               entries in [k].
%C A102539 T(n,k) is the number of k X k symmetric matrices with entries in 0..n 
               with each row (and column) in nondecreasing order. - Ron Hardin (rhhardin(AT)att.net), 
               Jul 08 2008
%H A102539 M. Lederer, <a href="http://arXiv.org/abs/math.CO/0501132">A determinant-like 
               formula for the Kostka numbers</a>
%F A102539 It appears that T is identical to the reflected triangle A073165, i.e. 
               T(n, k) = Prod[i=1..floor((k+1)/2), C(n+k+2i-1-(k mod 2), 4i-1-2(k 
               mod 2))] / Prod[i=0..floor((k-1)/2), C(2k-2i-1, 2i)].
%e A102539 2,4,8,16,32,64
%e A102539 3,10,35,126,462,1716
%e A102539 4,20,112,672,4224,27456
%e A102539 5,35,294,2772,28314,306735
%e A102539 6,56,672,9504,151008,2617472
%e A102539 7,84,1386,28314,674817,18076916
%Y A102539 Rows include A000079, A001700, A003645, A000356. Main diagonal is A049505.
%Y A102539 Sequence in context: A097093 A056877 A118263 this_sequence A118022 A037848 
               A037884
%Y A102539 Adjacent sequences: A102536 A102537 A102538 this_sequence A102540 A102541 
               A102542
%K A102539 nonn,tabl
%O A102539 1,1
%A A102539 Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 14 2005