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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 October 19 01:20 EDT 2019. Contains 328211 sequences. (Running on oeis4.)