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A161380 Triangle read by rows: T(n,k) = 2*k*T(n-1,n-1) + 1 (n >= 0, 0 <= k <= n), with T(0,0) = 1.

%I A161380 #16 Nov 25 2017 21:48:33
%S A161380 1,1,3,1,7,13,1,27,53,79,1,159,317,475,633,1,1267,2533,3799,5065,6331,
%T A161380 1,12663,25325,37987,50649,63311,75973,1,151947,303893,455839,607785,
%U A161380 759731,911677,1063623,1,2127247,4254493,6381739,8508985,10636231
%N A161380 Triangle read by rows: T(n,k) = 2*k*T(n-1,n-1) + 1 (n >= 0, 0 <= k <= n), with T(0,0) = 1.
%H A161380 Nathaniel Johnston, <a href="/A161380/b161380.txt">Table of n, a(n) for n = 0..2500</a>
%H A161380 Mathieu Guay-Paquet and Jeffrey Shallit, <a href="http://arxiv.org/abs/0901.1397">Avoiding Squares and Overlaps Over the Natural Numbers</a>, arXiv:0901.1397 [math.CO], 2009.
%H A161380 Mathieu Guay-Paquet and Jeffrey Shallit, <a href="https://doi.org/10.1016/j.disc.2009.06.004">Avoiding Squares and Overlaps Over the Natural Numbers</a>. Discrete Math., 309 (2009), 6245-6254.
%e A161380 Triangle begins:
%e A161380 1
%e A161380 1 3
%e A161380 1 7    13
%e A161380 1 27   53   79
%e A161380 1 159  317  475  633
%e A161380 1 1267 2533 3799 5065 6331
%p A161380 T := proc(n,k) option remember: if(n=0 and k=0)then return 1: else return 2*k*T(n-1,n-1)+1: fi: end:
%p A161380 for n from 0 to 8 do for k from 0 to n do printf("%d, ",T(n,k)): od: od: # _Nathaniel Johnston_, Apr 26 2011
%t A161380 T[0, 0] = 1; T[n_, k_] := 2*k*T[n - 1, n - 1] + 1;
%t A161380 Table[Table[T[n, k], {k, 0, n}], {n, 0, 8}] // Flatten (* _Jean-François Alcover_, Nov 25 2017 *)
%Y A161380 Diagonal gives A010844. Column 2 is A161370.
%K A161380 nonn,tabl,easy
%O A161380 0,3
%A A161380 _N. J. A. Sloane_, Nov 28 2009