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A158793
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Triangle read by rows: product of A130595 and A092392 considered as infinite lower triangular arrays.
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4
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1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 19, 9, 5, 1, 1, 51, 26, 11, 6, 1, 1, 141, 70, 34, 13, 7, 1, 1, 393, 197, 92, 43, 15, 8, 1, 1, 1107, 553, 265, 117, 53, 17, 9, 1, 1, 3139, 1570, 751, 346, 145, 64, 19, 10, 1, 1, 8953, 4476, 2156, 991, 441, 176, 76, 21, 11, 1, 1
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OFFSET
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0,4
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COMMENTS
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Matrix product P * Q * P^(-1), where P denotes Pascal's triangle A007318 and Q denotes A061554 (formed from P by sorting the rows into descending order). Cf. A158815 and A171243. - Peter Bala, Jul 13 2021
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LINKS
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FORMULA
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T(n, k) = (-1)^(k + n) binomial(n, k) hypergeom([k/2 + 1/2, k/2 + 1, k - n], [k + 1, k + 1], 4). - Peter Luschny, Jul 17 2021
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EXAMPLE
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First rows of the triangle:
1;
1, 1;
3, 1, 1;
7, 4, 1, 1;
19, 9, 5, 1, 1;
51, 26, 11, 6, 1, 1;
141, 70, 34, 13, 7, 1, 1;
393, 197, 92, 43, 15, 8, 1, 1;
1107, 553, 265, 117, 53, 17, 9, 1, 1;
3139, 1570, 751, 346, 145, 64, 19, 10, 1, 1;
8953, 4476, 2156, 991, 441, 176, 76, 21, 11, 1, 1;
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MAPLE
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add((-1)^(n+j)*binomial(n, j)*binomial(2*j-k, j-k), j = k..n);
end proc:
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MATHEMATICA
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T[n_, k_] := (-1)^(k + n) Binomial[n, k] HypergeometricPFQ[{k/2 + 1/2, k/2 + 1, k - n}, {k + 1, k + 1}, 4];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Peter Luschny, Jul 17 2021 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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