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Search: id:A136470
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| A136470 |
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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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+0
4
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| 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
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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FORMULA
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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).
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EXAMPLE
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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;
Column 0 of T^m is given by: [T^m](n,0) = C(m*2^n, n) for n>=0.
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PROGRAM
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(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]}
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CROSSREFS
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Cf. columns: A014070, A136471, A136472; A136467 (matrix square-root); A136462.
Sequence in context: A110608 A112007 A113374 this_sequence A138510 A026215 A026220
Adjacent sequences: A136467 A136468 A136469 this_sequence A136471 A136472 A136473
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2007
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