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A214178
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Triangle T(n,k) by rows: the k-th derivative of the Fibonacci Polynomial F_n(x) evaluated at x=1.
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3
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0, 1, 0, 1, 1, 0, 2, 2, 2, 0, 3, 5, 6, 6, 0, 5, 10, 18, 24, 24, 0, 8, 20, 44, 84, 120, 120, 0, 13, 38, 102, 240, 480, 720, 720, 0, 21, 71, 222, 630, 1560, 3240, 5040, 5040, 0, 34, 130, 466, 1536, 4560, 11760, 25200, 40320, 40320, 0, 55, 235, 948, 3564, 12264
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OFFSET
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0,7
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COMMENTS
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T(n,0) = A000045(n), Fibonacci numbers;
T(n,n) = 0.
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LINKS
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FORMULA
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T(n,k) = A037027(n,k)*k!, 0 <= k < n; T(n,n) = 0.
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EXAMPLE
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The triangle begins:
. 0: [0]
. 1: [1, 0]
. 2: [1, 1, 0]
. 3: [2, 2, 2, 0]
. 4: [3, 5, 6, 6, 0]
. 5: [5, 10, 18, 24, 24, 0]
. 6: [8, 20, 44, 84, 120, 120, 0]
. 7: [13, 38, 102, 240, 480, 720, 720, 0]
. 8: [21, 71, 222, 630, 1560, 3240, 5040, 5040, 0]
. 9: [34, 130, 466, 1536, 4560, 11760, 25200, 40320, 40320, 0]
. 10: [55, 235, 948, 3564, 12264, 37800, 100800, 221760, 362880, 362880, 0]
...
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MATHEMATICA
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T[n_, k_] := D[Fibonacci[n, x], {x, k}] /. x -> 1;
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PROG
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(Haskell)
a214178 n k = a214178_tabl !! n !! k
a214178_row n = a214178_tabl !! n
a214178_tabl = [0] : map f a037027_tabl where
f row = (zipWith (*) a000142_list row) ++ [0]
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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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