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%I #27 Aug 18 2022 08:29:25
%S 1,1,1,2,2,2,5,5,5,5,14,14,14,14,14,42,42,42,42,42,42,132,132,132,132,
%T 132,132,132,429,429,429,429,429,429,429,429,1430,1430,1430,1430,1430,
%U 1430,1430,1430,1430,4862,4862,4862,4862,4862,4862,4862,4862,4862,4862
%N Triangle read by rows: Catalan number C(n) repeated n+1 times.
%C As square array, it is A x B where A = square array A039599 (completed with zeros) and B = transpose of A. - _Philippe Deléham_, May 22 2015
%F T(n,k) = A000108(n). - _R. J. Mathar_, Nov 03 2016
%F G.f.: (x*C(x)-x*y*C(x*y))/(x-x*y), where C(x) is the g.f. of A000108. - _Vladimir Kruchinin_, Nov 19 2020
%F Sum_{n>=0} 1/a(n) = 4 + 28*Pi/(27*sqrt(3)). - _Amiram Eldar_, Aug 18 2022
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 2, 2;
%e 5, 5, 5, 5 ;
%e 14, 14, 14, 14, 14;
%e 42, 42, 42, 42, 42, 42;
%e From _Philippe Deléham_, May 22 2015: (Start)
%e A = square array A039599, completed with zeros.
%e 1.....0.....0.....0...
%e 1.....1.....0.....0...
%e 2.....3.....1.....0...
%e 5.....9.....5.....1...
%e ......................
%e B = transpose of A.
%e 1.....1.....2.....5...
%e 0.....1.....3.....9...
%e 0.....0.....1.....5...
%e 0.....0.....0.....1...
%e ......................
%e A x B = this sequence read as square array.
%e 1.....1.....2.....5...
%e 1.....2.....5....14...
%e 2.....5....14....42...
%e 5....14....42...132...
%e ...................... (End)
%t Table[PadRight[{}, n + 1, CatalanNumber[n]], {n, 0, 8}] // Flatten (* _Amiram Eldar_, Aug 18 2022, after _Harvey P. Dale_ at A172417 *)
%Y Cf. A000108, A000984 (row sums), A039599, A172414, A172417.
%K nonn,tabl,easy
%O 0,4
%A _Mark Dols_, Nov 21 2009
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