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A269956 Triangle read by rows, T(n,k) = binomial(3*n,n+k) for n>=0 and 0<=k<=n. 1
1, 3, 3, 15, 20, 15, 84, 126, 126, 84, 495, 792, 924, 792, 495, 3003, 5005, 6435, 6435, 5005, 3003, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Felix Fröhlich, Table of n, a(n) for n = 0..10000

FORMULA

T(n,0) = T(n,n) = A005809(n).

EXAMPLE

Triangle starts:

1,

3,    3,

15,   20,   15,

84,   126,  126,  84,

495,  792,  924,  792,  495,

3003, 5005, 6435, 6435, 5005, 3003

MAPLE

for n from 0 to 6 do seq(binomial(3*n, n+k), k=0..n) od;

MATHEMATICA

Table[Binomial[3 n, n + k], {n, 0, 10}, {k, 0, n}]//Flatten (* Vincenzo Librandi, Mar 28 2016 *)

PROG

(MAGMA) /* As triangle */ [[Binomial(3*n, n+k): k in [0..n]]: n in [0.. 7]]; // Vincenzo Librandi, Mar 28 2016

(PARI) t(n, k) = binomial(3*n, n+k)

trianglerows(n) = for(x=0, n-1, for(y=0, x, print1(t(x, y), ", ")); print(""))

/* The following function call prints the upper six rows of the triangle */

trianglerows(6) \\ Felix Fröhlich, Mar 28 2016

CROSSREFS

Cf. binomial(m*n,n+k): A000007 (m=0), A010054 (m=1), A094527 (m=2).

Cf. A005809.

Sequence in context: A110096 A157526 A208229 * A153512 A127328 A002891

Adjacent sequences:  A269953 A269954 A269955 * A269957 A269958 A269959

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Mar 28 2016

STATUS

approved

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Last modified July 24 23:25 EDT 2021. Contains 346273 sequences. (Running on oeis4.)