|
%I #12 Feb 18 2022 22:38:29
%S 1,2,1,4,4,1,8,11,6,1,16,26,22,8,1,32,57,64,37,10,1,64,120,163,130,56,
%T 12,1,128,247,382,386,232,79,14,1,256,502,848,1024,794,378,106,16,1,
%U 512,1013,1816,2510,2380,1471,576,137,18,1
%N A007318 * A004070.
%C Row sums = A061667: (1, 3, 9, 26, 73, 201, ...).
%C Companion triangle = A131249 = A007318 * A052509, where A052509 is the reversal of A004070.
%C Reversal of A097750. - _Philippe Deléham_, Jan 11 2014
%C Riordan array (1/(1-2x), x/(1-x)^2). - _Philippe Deléham_, Jan 11 2014
%C Diagonal sums are A045623. - _Philippe Deléham_, Jan 11 2014
%H Filippo Disanto, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Disanto/disanto5.html">Some Statistics on the Hypercubes of Catalan Permutations</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.2 (see Table 2).
%F Binomial transform of A004070.
%F T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0)=1, T(n,k)=0 if k < 0 or if k > n. - _Philippe Deléham_, Jan 11 2014
%e First few rows of the triangle:
%e 1;
%e 2, 1;
%e 4, 4, 1;
%e 8, 11, 6, 1;
%e 16, 26, 22, 8, 1;
%e 32, 57, 64, 37, 10, 1;
%e ...
%Y Cf. A004070, A061667, A131249, A007318.
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Jun 23 2007
%E More terms from _Philippe Deléham_, Jan 11 2014
|
