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A136470 Triangle T, read by rows, where column 0 of T^m = {C(m*2^n, n), n>=0} for all m. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..54.

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).

EXAMPLE

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.

PROG

(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(""))

CROSSREFS

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

Sequence in context: A190015 A112007 A113374 * A220884 A217877 A138510

Adjacent sequences:  A136467 A136468 A136469 * A136471 A136472 A136473

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Dec 31 2007

STATUS

approved

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Last modified August 2 02:27 EDT 2021. Contains 346408 sequences. (Running on oeis4.)