A133087 A133080 * A007318.
1, 2, 1, 1, 2, 1, 2, 5, 4, 1, 1, 4, 6, 4, 1, 2, 9, 16, 14, 6, 1, 1, 6, 15, 20, 15, 6, 1, 2, 13, 36, 55, 50, 27, 8, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 2, 17, 64, 140, 196, 182, 112, 44, 10, 1
Offset: 0
Examples
First few rows of the triangle: 1; 2, 1; 1, 2, 1; 2, 5, 4, 1; 1, 4, 6, 4, 1; 2, 9, 16, 14, 6, 1; 1, 6, 15, 20, 15, 6, 1; 2, 13, 36, 55, 50, 27, 8, 1; 1, 8, 28, 56, 70, 56, 28, 8, 1; ... Triangle (0, 2, -3/2, -1/2, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, ...) begins: 1; 0, 1; 0, 2, 1; 0, 1, 2, 1; 0, 2, 5, 4, 1; 0, 1, 4, 6, 4, 1; 0, 2, 9, 16, 14, 6, 1; 0, 1, 6, 15, 20, 15, 6, 1; 0, 2, 13, 36, 55, 50, 27, 8, 1; 0, 1, 8, 28, 56, 70, 56, 28, 8, 1; ...
Links
- G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Programs
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Mathematica
CoefficientList[CoefficientList[Series[(1 + 2*x + y*x)/(1 - (1 + y)^2*x^2), {x, 0, 10}, {y, 0, 10}], x], y] // Flatten (* G. C. Greubel, Oct 21 2017 *)
Formula
G.f.: (1+2*x+y*x)/(1-(1+y)^2*x^2). - Philippe Deléham, Mar 03 2012
T(n,k) = T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 1. - Philippe Deléham, Mar 03 2012
Comments