A139459 Triangle read by rows: binomial(3*n,3*k), 0 <= k <= n.

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

Offset

0,5

Comments

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

Row sums give A007613.

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:
[0] 1;
[1] 1,   1;
[2] 1,  20,     1;
[3] 1,  84,    84,     1;
[4] 1, 220,   924,   220,     1;
[5] 1, 455,  5005,  5005,   455,   1;
[6] 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,...).

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