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A100461 Triangle read by rows, based on array described below.

%I A100461 #8 Apr 07 2023 02:16:37
%S A100461 1,1,2,1,2,4,3,4,6,8,7,8,9,12,16,25,26,27,28,30,32,49,50,51,52,55,60,
%T A100461 64,109,110,111,112,115,120,126,128,229,230,231,232,235,240,245,248,
%U A100461 256,481,482,483,484,485,486,490,496,504,512,1003,1004,1005,1008,1010,1014,1015,1016,1017,1020,1024
%N A100461 Triangle read by rows, based on array described below.
%H A100461 G. C. Greubel, <a href="/A100461/b100461.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A100461 Form an array t(m,n) (n >= 1, 1 <= m <= n) by: t(1,n) = 2^(n-1) for all n; t(m+1,n) = (n-m)*floor( (t(m,n) - 1)/(n-m) ) for 1 <= m <= n-1.
%e A100461 Array begins:
%e A100461   1  2  4  8  16  32 ...
%e A100461   *  1  2  6  12  30 ...
%e A100461   *  *  1  4   9  28 ...
%e A100461   *  *  *  3   8  27 ...
%e A100461   *  *  *  *   7  26 ...
%e A100461   *  *  *  *   *  25 ...
%e A100461 and triangle begins:
%e A100461     1;
%e A100461     1,   2;
%e A100461     1,   2,   4;
%e A100461     3,   4,   6,   8;
%e A100461     7,   8,   9,  12,  16;
%e A100461    25,  26,  27,  28,  30,  32;
%e A100461    49,  50,  51,  52,  55,  60,  64;
%e A100461   109, 110, 111, 112, 115, 120, 126, 128;
%t A100461 t[n_, k_]:= t[n, k]= If[k==1, 2^(n-1), (n-k+1)*Floor[(t[n, k-1] -1)/(n-k+1)]];
%t A100461 Table[t[n, n-k+1], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Apr 07 2023 *)
%o A100461 (Magma)
%o A100461 function t(n,k) // t = A100461
%o A100461   if k eq 1 then return 2^(n-1);
%o A100461   else return (n-k+1)*Floor((t(n,k-1) -1)/(n-k+1));
%o A100461   end if;
%o A100461 end function;
%o A100461 [t(n,n-k+1): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 07 2023
%o A100461 (SageMath)
%o A100461 def t(n,k): # t = A100461
%o A100461     if (k==1): return 2^(n-1)
%o A100461     else: return (n-k+1)*((t(n, k-1) -1)//(n-k+1))
%o A100461 flatten([[t(n,n-k+1) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Apr 07 2023
%Y A100461 Cf. A100452, A100462, A119444.
%K A100461 nonn,tabl
%O A100461 1,3
%A A100461 _N. J. A. Sloane_, Nov 22 2004