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A281297 Triangular array of generalized Narayana numbers T(n,k) = 4*binomial(n+1,k)* binomial(n-4,k-1)/(n+1) for n >= 3 and 0 <= k <= n-3, read by rows. 2
1, 0, 4, 0, 4, 10, 0, 4, 24, 20, 0, 4, 42, 84, 35, 0, 4, 64, 224, 224, 56, 0, 4, 90, 480, 840, 504, 84, 0, 4, 120, 900, 2400, 2520, 1008, 120, 0, 4, 154, 1540, 5775, 9240, 6468, 1848, 165, 0, 4, 192, 2464, 12320, 27720, 29568, 14784, 3168, 220, 0, 4, 234, 3744, 24024, 72072, 108108, 82368, 30888, 5148 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

The current array is the case m = 3 of the generalized Narayana numbers N_m(n,k) := (m+1)/(n+1)*binomial(n+1,k)*binomial(n-m-1,k-1) for m >= 0, n >= m and 0 <= k <= n-m with N_m(n,0) = A000007(n-m). Case m = 0 gives the table of Narayana numbers A001263 without leading column N_0(n,0) = A000007(n). For m = 1 see A281260, and for m = 2 see A281293.

LINKS

Table of n, a(n) for n=3..67.

David Callan, Generalized Narayana Numbers .

FORMULA

Row sums are A033184(n+1,4).

G.f.: A(x) = x*A281260(x,y)^2. - Vladimir Kruchinin, Oct 10 2020

EXAMPLE

The triangle begins:

n\k:  0  1    2     3      4      5       6      7      8     9   10  . . .

03 :  1

04 :  0  4

05 :  0  4   10

06 :  0  4   24    20

07 :  0  4   42    84     35

08 :  0  4   64   224    224     56

09 :  0  4   90   480    840    504      84

10 :  0  4  120   900   2400   2520    1008    120

11 :  0  4  154  1540   5775   9240    6468   1848    165

12 :  0  4  192  2464  12320  27720   29568  14784   3168   220

13 :  0  4  234  3744  24024  72072  108108  82368  30888  5148  286

etc.

CROSSREFS

Cf. A000007, A001263, A033184, A281260, A281293.

Sequence in context: A200341 A101980 A209134 * A058536 A154854 A151672

Adjacent sequences:  A281294 A281295 A281296 * A281298 A281299 A281300

KEYWORD

nonn,tabl,easy

AUTHOR

Werner Schulte, Jan 19 2017

STATUS

approved

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Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)