A136470 Triangle T, read by rows, where column 0 of T^m = {C(m*2^n, n), n>=0} for all m.

1, 2, 1, 6, 8, 1, 56, 128, 32, 1, 1820, 6048, 2176, 128, 1, 201376, 912128, 419328, 34816, 512, 1, 74974368, 449708544, 249300992, 26198016, 548864, 2048, 1, 94525795200, 739136655360, 477013868544, 59943682048, 1604059136, 8650752, 8192, 1, 409663695276000, 4132411271661568, 3028532448264192, 439222754869248, 14159357935616, 98723430400, 136839168, 32768, 1, 6208116950265950720, 80121787455478857728, 65415571433959456768, 10679727629898088448, 399723620798038016, 3391703461396480, 6141702569984, 2172649472, 131072, 1

Offset: 0

Author

Paul D. Hanna, Dec 31 2007

Keywords

• nonn
• tabl

Comments

Column 0 of T^(n+1) = row 2n+1 of square array A136462 defined by: A136462(n,k) = C((n+1)*2^(k-1), k); T^n denotes the n-th matrix power of this triangle T = A136470.

Examples

			Triangle T begins:
1;
2, 1;
6, 8, 1;
56, 128, 32, 1;
1820, 6048, 2176, 128, 1;
201376, 912128, 419328, 34816, 512, 1;
74974368, 449708544, 249300992, 26198016, 548864, 2048, 1;
94525795200, 739136655360, 477013868544, 59943682048, 1604059136, 8650752, 8192, 1;
409663695276000, 4132411271661568, 3028532448264192, 439222754869248, 14159357935616, 98723430400, 136839168, 32768, 1; ...
Column 0 of T^m is given by: [T^m](n,0) = C(m*2^n, n) for n>=0.
		

Crossrefs

Cf. columns: A014070, A136471, A136472; A136467 (matrix square-root); A136462.

Programs

PARI

{T(n,k)=local(M=matrix(n+1,n+1,r,c,binomial(r*2^(c-2),c-1)),P); P=matrix(n+1,n+1,r,c,binomial((r+1)*2^(c-2),c-1));((P~*M~^-1)^2)[n+1,k+1]}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))

Formula

Equals the matrix square of triangle A136467.

Diagonals: T(n+1,n) = 2*4^n; T(n+2,n) = 2*8^n*(2^(n+2) + n-1).