This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A139459 #30 Jun 01 2025 03:43:41
%S A139459 1,1,1,1,20,1,1,84,84,1,1,220,924,220,1,1,455,5005,5005,455,1,1,816,
%T A139459 18564,48620,18564,816,1,1,1330,54264,293930,293930,54264,1330,1,1,
%U A139459 2024,134596,1307504,2704156,1307504,134596,2024,1,1,2925,296010,4686825,17383860,17383860,4686825,296010,2925,1
%N A139459 Triangle read by rows: binomial(3*n,3*k), 0 <= k <= n.
%C A139459 ConvOffsStoT transform of the dodecahedral numbers A006566 starting (1, 20, 84, 220,...).
%C A139459 Row sums give A007613.
%C A139459 The matrix inverse starts:
%C A139459 1;
%C A139459 -1,1;
%C A139459 19,-20,1;
%C A139459 -1513,1596,-84,1;
%C A139459 315523,-332860,17556,-220,1;
%C A139459 -136085041,143562965,-7572565,95095,-455,1;
%C A139459 105261234643,-111045393456,5857368972,-73562060,352716,-816,1; - _R. J. Mathar_, Mar 22 2013
%e A139459 First few rows of the triangle are:
%e A139459 [0] 1;
%e A139459 [1] 1, 1;
%e A139459 [2] 1, 20, 1;
%e A139459 [3] 1, 84, 84, 1;
%e A139459 [4] 1, 220, 924, 220, 1;
%e A139459 [5] 1, 455, 5005, 5005, 455, 1;
%e A139459 [6] 1, 816, 18564, 48620, 18564, 816, 1;
%e A139459 ...
%e A139459 Row 5 = (1, 220, 924, 220, 1) = ConvOffs transform of (1, 20, 84, 220); where A006566 = (0, 1, 20, 84, 220, 455, ...).
%t A139459 Table[Binomial[3*n, 3*k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Jun 01 2025 *)
%Y A139459 Cf. A006566, A007613, A086645, A034839, A070775, A177808.
%K A139459 nonn,easy,tabl
%O A139459 0,5
%A A139459 _Gary W. Adamson_, Apr 22 2008
%E A139459 More terms from _Amiram Eldar_, Jun 01 2025