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A166454 Triangle read by rows: T(n, k) = (1/2)*(A007318(n,k) - A047999(n,k)).

%I A166454 #24 Sep 08 2022 08:45:48
%S A166454 1,1,1,2,3,2,2,5,5,2,3,7,10,7,3,3,10,17,17,10,3,4,14,28,35,28,14,4,4,
%T A166454 18,42,63,63,42,18,4,5,22,60,105,126,105,60,22,5,5,27,82,165,231,231,
%U A166454 165,82,27,5,6,33,110,247,396,462,396,247,110,33,6
%N A166454 Triangle read by rows: T(n, k) = (1/2)*(A007318(n,k) - A047999(n,k)).
%C A166454 Row sums = A120739: (1, 2, 7, 14, 30, 60, 127, 254, ...).
%H A166454 Reinhard Zumkeller, <a href="/A166454/b166454.txt">Rows n = 2..125 of triangle, flattened</a>
%F A166454 T(n, k) = (1/2)*(A007318(n,k) - A047999(n,k)), nonzero terms.
%F A166454 T(n, m) = floor(binomial(n, m)/2). - _Roger L. Bagula_, Mar 07 2010
%e A166454 First few rows of the triangle:
%e A166454   1;
%e A166454   1,   1;
%e A166454   2,   3,   2;
%e A166454   2,   5,   5,   2;
%e A166454   3,   7,  10,   7,   3;
%e A166454   3,  10,  17,  17,  10,   3;
%e A166454   4,  14,  28,  35,  28,  14,   4;
%e A166454   4,  18,  42,  63,  63,  42,  18,   4;
%e A166454   5,  22,  60, 105, 126, 105,  60,  22,   5;
%e A166454   5,  27,  82, 165, 231, 231, 165,  82,  27,   5;
%e A166454   6,  33, 110, 247, 396, 462, 396, 247, 110,  33,   6;
%e A166454   ...
%p A166454 seq(seq(floor(binomial(n,m)/2),m=1..n-1),n=2..12); # _Muniru A Asiru_, Apr 14 2019
%t A166454 T[n_, m_] = Floor[Binomial[n, m]/2]; Table[T[n, m], {n, 2, 12}, {m, 1, n-1}]//Flatten (* _Roger L. Bagula_, Mar 07 2010*)
%o A166454 (Haskell)  Following Bagula's formula
%o A166454 a166454 n k = a166454_tabl !! (n-2) !! (k-1)
%o A166454 a166454_row n = a166454_tabl !! (n-2)
%o A166454 a166454_tabl = map (map (flip div 2) . init . tail) $ drop 2 a007318_tabl
%o A166454 -- _Reinhard Zumkeller_, Mar 04 2015
%o A166454 (GAP) Flat(List([2..12],n->List([1..n-1],m->Int(Binomial(n,m)/2)))); # _Muniru A Asiru_, Apr 14 2019
%o A166454 (PARI) {T(n,k) = binomial(n,k)\2 };
%o A166454 for(n=2,12, for(k=1,n-1, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Apr 16 2019
%o A166454 (Magma) [[Floor(Binomial(n,k)/2): k in [1..n-1]]: n in [2..12]]; // _G. C. Greubel_, Apr 16 2019
%o A166454 (Sage) [[floor(binomial(n,k)/2) for k in (1..n-1)] for n in (2..12)] # _G. C. Greubel_, Apr 16 2019
%Y A166454 Cf. A047999, A120739.
%Y A166454 Cf. A007318, A011848, A001700 (central terms).
%K A166454 nonn,tabl
%O A166454 2,4
%A A166454 _Gary W. Adamson_, Oct 14 2009