%I A126445
%S A126445 1,1,1,6,3,1,120,36,6,1,4845,969,120,10,1,324632,46376,4495,300,15,1,
%T A126445 32468436,3478761,270725,15180,630,21,1,4529365776,377447148,24040016,
%U A126445 1150626,41664,1176,28,1,840261910995,56017460733,2967205528,122391522
%N A126445 Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3), n-k) for 
               n>=k>=0.
%C A126445 Amazingly, A126460 = A126445^-1*A126450 = A126450^-1*A126454 = A126454^-1*A126457; 
               and also A126465 = A126450*A126445^-1 = A126454*A126450^-1 = A126457*A126454^-1.
%F A126445 T(n,k) = C( n*(n+1)*(n+2)/3! - k*(k+1)*(k+2)/3!, n-k) for n>=k>=0.
%e A126445 Formula: T(n,k) = C( C(n+2,3) - C(k+2,3), n-k) is illustrated by:
%e A126445 T(n=4,k=1) = C( C(6,3) - C(3,3), n-k) = C(19,3) = 969;
%e A126445 T(n=4,k=2) = C( C(6,3) - C(4,3), n-k) = C(16,2) = 120;
%e A126445 T(n=5,k=2) = C( C(7,3) - C(4,3), n-k) = C(31,3) = 4495.
%e A126445 Triangle begins:
%e A126445 1;
%e A126445 1, 1;
%e A126445 6, 3, 1;
%e A126445 120, 36, 6, 1;
%e A126445 4845, 969, 120, 10, 1;
%e A126445 324632, 46376, 4495, 300, 15, 1;
%e A126445 32468436, 3478761, 270725, 15180, 630, 21, 1;
%e A126445 4529365776, 377447148, 24040016, 1150626, 41664, 1176, 28, 1; ...
%o A126445 (PARI) T(n,k)=binomial(n*(n+1)*(n+2)/3!-k*(k+1)*(k+2)/3!, n-k)
%Y A126445 Columns: A126446, A126447, A126448; A126449 (row sums); variants: A126450, 
               A126454, A126457, A107862.
%Y A126445 Sequence in context: A119743 A108451 A122178 this_sequence A033326 A068996 
               A068924
%Y A126445 Adjacent sequences: A126442 A126443 A126444 this_sequence A126446 A126447 
               A126448
%K A126445 nonn,tabl
%O A126445 0,4
%A A126445 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 27 2006