0,5

Antidiagonal sums form A093542. Main diagonal is A093543.

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.

Column 2: {1,4,12,28,56,100,...} equals the self-convolution of row 1: {1,2,4,6,8,10,...}.

Rows begin:

[1,1,1,1,1,1,1,1,1,1,1,1,1,...],

[1,2,4,6,8,10,12,14,16,18,20,22,...],

[1,3,12,33,72,137,236,377,568,817,...],

[1,4,28,138,500,1532,4196,10518,...],

[1,5,56,486,2888,13772,57560,219834,...],

[1,6,100,1498,14792,110856,698816,...],

[1,7,164,4111,67692,812492,7930308,...],

[1,8,252,10210,278396,5364868,...],

[1,9,368,23288,1040856,31939300,...],

[1,10,516,49394,3581120,173226000,...],...

(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))))

Cf. A093542, A093543.

Sequence in context: A111669 A124834 A104495 this_sequence A089940 A123974 A056863

Adjacent sequences: A093538 A093539 A093540 this_sequence A093542 A093543 A093544

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 30 2004