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.

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, 100, 486, 500, 137, 12, 1, 1, 8, 164, 1498, 2888, 1532, 236, 14, 1, 1, 9, 252, 4111, 14792, 13772, 4196, 377, 16, 1, 1, 10, 368, 10210, 67692, 110856, 57560, 10518, 568

Offset

0,5

Comments

Antidiagonal sums form A093542. Main diagonal is A093543.

Links

Table of n, a(n) for n=0..63.

Formula

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.

Example

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,...],...

Prog

(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))))

Crossrefs

Cf. A093542, A093543.

Sequence in context: A124834 A271465 A104495 * A336187 A171881 A321877

Adjacent sequences: A093538 A093539 A093540 * A093542 A093543 A093544

Keyword

nonn,tabl

Author

Paul D. Hanna, Mar 30 2004

Status

approved