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 A214178 Triangle T(n,k) by rows: the k-th derivative of the Fibonacci Polynomial F_n(x) evaluated at x=1. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS T(n,0) = A000045(n), Fibonacci numbers; T(n,1) = A001629(n) for n > 0; T(n,n-3) = A038720(n-2) for n > 2; T(n,n-2) = A000142(n-1) for n > 1; T(n,n-1) = A000142(n-1) for n > 0; T(n,n) = 0. LINKS Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened P. Filipponi, A. F. Horadam, Second derivative sequences of Fibonacci and Lucas Polynomials, Fib. Quart. 31 (1993), 194-204. FORMULA T(n,k) = A037027(n,k)*k!, 0 <= k < n; T(n,n) = 0. EXAMPLE 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]        ... PROG (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] CROSSREFS Cf. A000142, A037027. Sequence in context: A124759 A071295 A296062 * A117652 A103223 A091399 Adjacent sequences:  A214175 A214176 A214177 * A214179 A214180 A214181 KEYWORD nonn,tabl AUTHOR R. J. Mathar, L. Edson Jeffery, Reinhard Zumkeller, Jul 07 2012 STATUS approved

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Last modified April 21 17:34 EDT 2021. Contains 343156 sequences. (Running on oeis4.)