%I A093541
%S A093541 1,1,1,1,2,1,1,3,4,1,1,4,12,6,1,1,5,28,33,8,1,1,6,56,138,72,10,1,1,7,
%T A093541 100,486,500,137,12,1,1,8,164,1498,2888,1532,236,14,1,1,9,252,4111,
%U A093541 14792,13772,4196,377,16,1,1,10,368,10210,67692,110856,57560,10518,568
%N A093541 Square array, read by antidiagonals, where column (k+1) equals the self-convolution 
               of row k, with row 0 and column 0 consisting of all 1's.
%C A093541 Antidiagonal sums form A093542. Main diagonal is A093543.
%F A093541 T(n, k) = sum_{i=0..n} T(k-1, i)*T(k-1, n-i), with T(n, 0)=T(0, k)=1 
               for n>=0, k>0.
%e A093541 Column 2: {1,4,12,28,56,100,...} equals the self-convolution of row 1: 
               {1,2,4,6,8,10,...}.
%e A093541 Rows begin:
%e A093541 [1,1,1,1,1,1,1,1,1,1,1,1,1,...],
%e A093541 [1,2,4,6,8,10,12,14,16,18,20,22,...],
%e A093541 [1,3,12,33,72,137,236,377,568,817,...],
%e A093541 [1,4,28,138,500,1532,4196,10518,...],
%e A093541 [1,5,56,486,2888,13772,57560,219834,...],
%e A093541 [1,6,100,1498,14792,110856,698816,...],
%e A093541 [1,7,164,4111,67692,812492,7930308,...],
%e A093541 [1,8,252,10210,278396,5364868,...],
%e A093541 [1,9,368,23288,1040856,31939300,...],
%e A093541 [1,10,516,49394,3581120,173226000,...],...
%o A093541 (PARI) T(n,k)=if(n<0|k<0,0,if(n==0|k==0,1,sum(i=0,n,T(k-1,i)*T(k-1,n-i))))
%Y A093541 Cf. A093542, A093543.
%Y A093541 Sequence in context: A111669 A124834 A104495 this_sequence A089940 A123974 
               A056863
%Y A093541 Adjacent sequences: A093538 A093539 A093540 this_sequence A093542 A093543 
               A093544
%K A093541 nonn,tabl
%O A093541 0,5
%A A093541 Paul D. Hanna (pauldhanna(AT)juno.com), Mar 30 2004