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A140982
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If (a_n) is a sequence then let L(a_n)=(b_n) where b_n = a_n^2 - a_{n-1} a_{n+1}. The given sequence is the rows of the triangle obtained by computing L^2(binomial(n,k)).
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0
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1, 3, 1, 6, 16, 1, 10, 100, 50, 1, 15, 400, 750, 120, 1, 21, 1225, 6125, 3675, 245, 1, 28, 3136, 34300, 54880, 13720, 448, 1, 36, 7056, 148176, 518616, 345744, 42336, 756, 1, 45, 14400, 529200, 3556224, 5186160, 1693440, 113400, 1200, 1, 55, 27225, 1633500
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OFFSET
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3,2
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COMMENTS
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L(binomial(n,k)) gives the Narayana numbers, A001263.
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LINKS
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FORMULA
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a(n,k) = binomial(n,k)^2 * binomial(n,k-1) * binomial(n,k-2) / (n*binomial(n,2)).
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MATHEMATICA
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a[n_, k_] := 2 * Binomial[n, k]^2 * Binomial[n, k - 1] * Binomial[n, k - 2] / ((n - 1) n^2); Table[ a[n, k], {n, 2, 11}, {k, 2, n}] // Flatten (* Robert G. Wilson v, Aug 03 2008 *)
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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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