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A120257 Triangle of Hankel transforms of certain binomial sums. 1
1, 2, -1, 3, -6, -1, 4, -20, -20, 1, 5, -50, -175, 70, 1, 6, -105, -980, 1764, 252, -1, 7, -196, -4116, 24696, 19404, -924, -1, 8, -336, -14112, 232848, 731808, -226512, -3432, 1, 9, -540, -41580, 1646568, 16818516, -24293412, -2760615, 12870, 1, 10, -825, -108900, 9343620, 267227532, -1447482465 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row k is the Hankel transform of sum{j=0..n, C(k+j, j)}. Absolute value is reversal of A103905. Diagonal and sub-diagonals are essentially signed versions of the central coefficients of certain generalized Pascal-Narayana triangles (A007318, A001263, A056939, A056940, A056941).

LINKS

Table of n, a(n) for n=0..50.

FORMULA

T(n, k):=(cos(pi*k/2)-sin(pi*k/2))*product{j=0..n-k-1, C(2k+2+j, k+1)/C(k+1+j, j)}

EXAMPLE

Triangle begins

1,

2, -1,

3, -6, -1,

4, -20, -20, 1,

5, -50, -175, 70, 1,

6, -105, -980, 1764, 252, -1,

7, -196, -4116, 24696, 19404, -924, -1,

8, -336, -14112, 232848, 731808, -226512, -3432, 1

CROSSREFS

Cf. A120258.

Sequence in context: A325007 A103371 A325015 * A059298 A214306 A156914

Adjacent sequences:  A120254 A120255 A120256 * A120258 A120259 A120260

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Jun 13 2006

STATUS

approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)