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%I #25 Mar 18 2023 09:06:35
%S 1,1,1,1,20,1,1,84,84,1,1,220,924,220,1,1,455,5005,5005,455,1,1,816,
%T 18564,48620,18564,816,1,1,1330,54264,293930,293930,54264,1330,1
%N Triangle read by rows: binomial(3*n,3*k), 0 <= k <= n.
%C ConvOffsStoT transform of the dodecahedral numbers A006566 starting (1, 20, 84, 220,...)
%C Row sums give A007613.
%C The matrix inverse starts:
%C 1;
%C -1,1;
%C 19,-20,1;
%C -1513,1596,-84,1;
%C 315523,-332860,17556,-220,1;
%C -136085041,143562965,-7572565,95095,-455,1;
%C 105261234643,-111045393456,5857368972,-73562060,352716,-816,1; - _R. J. Mathar_, Mar 22 2013
%e First few rows of the triangle are:
%e [0] 1;
%e [1] 1, 1;
%e [2] 1, 20, 1;
%e [3] 1, 84, 84, 1;
%e [4] 1, 220, 924, 220, 1;
%e [5] 1, 455, 5005, 5005, 455, 1;
%e [6] 1, 816, 18564, 48620, 18564, 816, 1;
%e ...
%e Row 5 = (1, 220, 924, 220, 1) = ConvOffs transform of (1, 20, 84, 220); where A006566 = (0, 1, 20, 84, 220, 455,...).
%Y Cf. A006566, A007613, A086645, A034839, A070775, A177808.
%K nonn,easy,tabl
%O 0,5
%A _Gary W. Adamson_, Apr 22 2008
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