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A326832
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Triangle read by rows: T(n, k) = (-1)^(n - k) * binomial(2n + 1, n - k) * L(2k + 1), 0 <= k <= n, where L(k) is the k-th Lucas number (A000032).
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0
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1, -3, 4, 10, -20, 11, -35, 84, -77, 29, 126, -336, 396, -261, 76, -462, 1320, -1815, 1595, -836, 199, 1716, -5148, 7865, -8294, 5928, -2587, 521, -6435, 20020, -33033, 39585, -34580, 20895, -7815, 1364, 24310, -77792, 136136, -179452, 180880, -135320, 70856, -23188, 3571
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OFFSET
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0,2
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COMMENTS
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This triangle is the subject of the paper by Agarwal (1990).
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LINKS
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FORMULA
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Sum_{k=0..n} T(n, k) = 1.
T(n + 1, k) = -(2n + 3)*(2n + 2)/((n - k + 1)*(n + k + 2)) * T(n, k).
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MATHEMATICA
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T[n_, k_] := (-1)^(n - k) * Binomial[2 n + 1, n - k] * LucasL[2 k + 1]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten
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PROG
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(PARI) L(n) = fibonacci(n+1) + fibonacci(n-1); \\ A000032
T(n, k) = (-1)^(n - k) * binomial(2*n + 1, n - k) * L(2*k + 1); \\ Michel Marcus, Oct 21 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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