A155042 Row sums of A155039.
0, 1, 2, 5, 9, 21, 39, 82, 162, 330, 652, 1321, 2625
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
T(5,2) = 4 because the compositions of 5 with first part 2 are: [2,3], [2,2,1], [2,1,2], and [2,1,1,1]. - _Emeric Deutsch_, Jan 12 2018 Table begins: 1, 1, 1, 2, 1, 1, 4, 2, 1, 1, 8, 4, 2, 1, 1, 16, 8, 4, 2, 1, 1, 32, 16, 8, 4, 2, 1, 1, 64, 32, 16, 8, 4, 2, 1, 1, Production matrix begins: 1, 1 1, 0, 1 1, 0, 0, 1 1, 0, 0, 0, 1 1, 0, 0, 0, 0, 1 1, 0, 0, 0, 0, 0, 1 1, 0, 0, 0, 0, 0, 0, 1 1, 0, 0, 0, 0, 0, 0, 0, 1 ... - _Philippe Deléham_, Oct 04 2014
a155038 n k = a155038_tabl !! (n-1) !! (k-1) a155038_row n = a155038_tabl !! (n-1) a155038_tabl = iterate (\row -> zipWith (+) (row ++ [0]) (init row ++ [0,1])) [1] -- Reinhard Zumkeller, Aug 08 2013
T := proc(n, k) if k = n then 1 elif k < n then 2^(n-k-1) else 0 end if end proc: for n to 13 do seq(T(n, k), k = 1 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jan 12 2018 G:= (1-2*x+t*x^2)/((1-2*x)*(1-t*x)): Gser := simplify(series(G, x = 0, 15)): for n to 14 do P[n] := coeff(Gser, x, n) end do: for n to 14 do seq(coeff(P[n], t, j), j = 1 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jan 19 2018
nn = 15; a = 1/(1 - y x); f[list_] := Select[list, # > 0 &];Map[f, CoefficientList[Series[ a/(1 - x/(1 - x)), {x, 0, nn}], {x, y}]] // Flatten (* Geoffrey Critzer, Feb 15 2012 *)
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