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A214281 Triangle by rows, row n contains the ConvOffs transform of the first n terms of 1, 1, 3, 2, 5, 3, 7, ... (A026741 without leading zero).

%I A214281 #14 Feb 08 2022 22:16:07
%S A214281 1,1,1,1,1,1,1,3,3,1,1,2,6,2,1,1,5,10,10,5,1,1,3,15,10,15,3,1,1,7,21,
%T A214281 35,35,21,7,1,1,4,28,28,70,28,28,4,1,1,9,36,84,126,126,84,36,9,1,1,5,
%U A214281 45,60,210,126,210,60,45,5,1,1,11,55,165,330,462,462,330,165,55,11,1
%N A214281 Triangle by rows, row n contains the ConvOffs transform of the first n terms of 1, 1, 3, 2, 5, 3, 7, ... (A026741 without leading zero).
%C A214281 The ConvOffs transform of a sequence s(0), s(1), ..., s(t-1) is defined by a(0)=1 and a(n) = a(n-1)*s(t-n)/s(n-1) for 1 <= n < t. An example of this process is also shown in the Narayana triangle, A001263. By increasing the length t of the input sequence (here: A026741) we create more and more rows of the triangle.
%H A214281 Tom Edgar and Michael Z. Spivey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Edgar/edgar3.html">Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.
%F A214281 T(n,k) = binomial(n,k) if n is odd.
%e A214281 First few rows of the triangle:
%e A214281   1;
%e A214281   1,  1;
%e A214281   1,  1,  1;
%e A214281   1,  3,  3,   1;
%e A214281   1,  2,  6,   2,   1;
%e A214281   1,  5, 10,  10,   5,   1;
%e A214281   1,  3, 15,  10,  15,   3,   1;
%e A214281   1,  7, 21,  35,  35,  21,   7,   1;
%e A214281   1,  4, 28,  28,  70,  28,  28,   4,   1;
%e A214281   1,  9, 36,  84, 126, 126,  84,  36,   9,  1;
%e A214281   1,  5, 45,  60, 210, 126, 210,  60,  45,  5,  1;
%e A214281   1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1;
%e A214281   ...
%Y A214281 Cf. A134683 (row sums), A026741, A001263.
%K A214281 nonn,tabl,easy
%O A214281 0,8
%A A214281 _Gary W. Adamson_, Jul 09 2012