A136471 -id:A136471 - cp's OEIS frontend

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

Paul D. Hanna, Dec 31 2007

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.

			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.

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

{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(""))

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).

A136472 Column 2 of triangle A136470 (scaled): a(n) = A136470(n+2,2)/4^n.

Original entry on oeis.org

1, 8, 136, 6552, 973832, 465833856, 739387804752, 3992649623654752, 74888425049167499424, 4962998789388515787006336, 1178375010889854741001146703936, 1013755301703927988518902015091910656

Offset: 0

Paul D. Hanna, Jan 01 2008

nonn

Triangle T = A136470 is defined by: column 0 of T^m = {C(m*2^n, n), n>=0}.

Cf. A136470; A136471.

{a(n)=local(M=matrix(n+3,n+3,r,c,binomial(r*2^(c-1),c-1)),P); P=matrix(n+3,n+3,r,c,binomial((r+1)*2^(c-1),c-1));(P~*M~^-1)[n+3,3]/4^n}

cp's OEIS Frontend

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

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