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A139459 Triangle read by rows: binomial(3*n,3*k), 0 <= k <= n. 3
1, 1, 1, 1, 20, 1, 1, 84, 84, 1, 1, 220, 924, 220, 1, 1, 455, 5005, 5005, 455, 1, 1, 816, 18564, 48620, 18564, 816, 1, 1, 1330, 54264, 293930, 293930, 54264, 1330, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

ConvOffsStoT transform of the dodecahedral numbers A006566 starting (1, 20, 84, 220,...)

Row sums = A007613(n-1).

One of the set of triangles Binomial(k*n,k*m),k=1,2,3,4,... [Roger L. Bagula, Dec 12 2010]

The matrix inverse starts:

1;

-1,1;

19,-20,1;

-1513,1596,-84,1;

315523,-332860,17556,-220,1;

-136085041,143562965,-7572565,95095,-455,1;

105261234643,-111045393456,5857368972,-73562060,352716,-816,1; - R. J. Mathar, Mar 22 2013

LINKS

Table of n, a(n) for n=0..35.

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

1, 20, 1;

1, 84, 84, 1;

1, 220, 924, 220, 1;

1, 455, 5005, 5005, 455, 1;

1, 816, 18564, 48620, 18564, 816, 1;

...

Row 5 = (1, 220, 924, 220, 1) = ConvOffs transform of (1, 20, 84, 220); where A006566 = (0, 1, 20, 84, 220, 455,...).

MATHEMATICA

t[n_, m_] = Binomial[n, 3*m];

Table[Table[t[n, m], {m, 0, Floor[n/3]}], {n, 0, 30, 3}];

Flatten[%] (* Roger L. Bagula, Dec 12 2010 *)

CROSSREFS

Cf. A006566, A007613, A086645, A034839, A070775, A177808.

Sequence in context: A040402 A040401 A040400 * A154652 A155516 A174674

Adjacent sequences:  A139456 A139457 A139458 * A139460 A139461 A139462

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Apr 22 2008

STATUS

approved

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)