A181690 Riordan array T((1-x)^(-2) | 2x-1) read by rows.
-1, -4, 1, -11, 6, -1, -26, 23, -8, 1, -57, 72, -39, 10, -1, -120, 201, -150, 59, -12, 1, -247, 522, -501, 268, -83, 14, -1, -502, 1291, -1524, 1037, -434, 111, -16, 1, -1013, 3084, -4339, 3598, -1905, 656, -143, 18, -1, -2036, 7181, -11762, 11535, -7408, 3217, -942, 179, -20, 1
Offset: 0
Examples
Array begins:
-1;
-4, 1;
-11, 6, -1;
-26, 23, -8, 1;
-57, 72, -39, 10, -1;
-120, 201, -150, 59, -12, 1;
...
Links
- Ana Luzón, Iterative Processes Related to Riordan Arrays: The Reciprocation and the Inversion of Power Series, arXiv:0907.2328 [math.CO], 2009-2010; Discrete Math., 310 (2010), 3607-3618.
- Ana Luzón and Manuel A. Morón, Riordan matrices in the reciprocation of quadratic polynomials, Linear Algebra Appl. 430 (2009), no. 8-9, 22542270.
Programs
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Mathematica
t[n_, k_] := t[n, k] = If[n<0, 0, If[k==0, n+3-2^(n+2), If[k>n, 0, 2 t[n-1, k] - t[n-1, k-1]]]]; Table[t[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 24 2018, from PARI *) -
PARI
t(n, k) = if (n < 0, 0, if (k == 0, n + 3 - 2^(n+2), if (k >n, 0, 2*tr(n-1, k) - tr(n-1, k-1)))); \\ Michel Marcus, Feb 14 2014
Extensions
a(0) corrected and more terms from Michel Marcus, Feb 14 2014
Comments