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%I #11 Jan 17 2024 17:10:10
%S 1,3,6,5,10,20,7,14,28,56,9,18,36,72,144,11,22,44,88,176,352,13,26,52,
%T 104,208,416,832,15,30,60,120,240,480,960,1920,17,34,68,136,272,544,
%U 1088,2176,4352,19,38,76,152,304,608,1216,2432,4864,9728,21,42,84,168
%N Triangle read by rows: T(n,k) = (2*n-1)*2^(k-1), 0<k<=n.
%C Central terms give A118415; row sums give A118414;
%C T(n,1) = A005408(n-1);
%C T(n,2) = A016825(n-1) for n>1;
%C T(n,3) = A017113(n-1) for n>2;
%C T(n,4) = A051062(n-1) for n>3;
%C T(n,n-2) = A052951(n-1) for n>2;
%C T(n,n) = A014480(n-1) = A118416(n,n);
%C A001511(T(n,k)) = A002260(n,k);
%C A003602(T(n,k)) = A002024(n,k).
%e 1
%e 3 6
%e 5 10 20
%e 7 14 28 56
%e 9 18 36 72 144
%e 11 22 44 88 176 352
%e 13 26 52 104 208 416 832
%e 15 30 60 120 240 480 960 1920
%e 17 34 68 136 272 544 1088 2176 4352
%e 19 38 76 152 304 608 1216 2432 4864 9728
%t Select[Flatten[Table[(2n-1)2^(k-1),{n,20},{k,0,n}]],IntegerQ] (* _Harvey P. Dale_, Jan 17 2024 *)
%Y Cf. A118416, A117303.
%K nonn,tabl,easy
%O 1,2
%A _Reinhard Zumkeller_, Apr 27 2006
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