A144393 Triangle read by rows (n >= 0, 0 <= k <= n): row n gives the coefficients in the expansion of x^n + n*x^(n - 1) + n*x + 1.
2, 2, 2, 1, 4, 1, 1, 3, 3, 1, 1, 4, 0, 4, 1, 1, 5, 0, 0, 5, 1, 1, 6, 0, 0, 0, 6, 1, 1, 7, 0, 0, 0, 0, 7, 1, 1, 8, 0, 0, 0, 0, 0, 8, 1, 1, 9, 0, 0, 0, 0, 0, 0, 9, 1, 1, 10, 0, 0, 0, 0, 0, 0, 0, 10, 1, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 11, 1, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1
Offset: 0
Examples
Triangle begins: 2; 2, 2; 1, 4, 1; 1, 3, 3, 1; 1, 4, 0, 4, 1; 1, 5, 0, 0, 5, 1; 1, 6, 0, 0, 0, 6, 1; 1, 7, 0, 0, 0, 0, 7, 1; 1, 8, 0, 0, 0, 0, 0, 8, 1; 1, 9, 0, 0, 0, 0, 0, 0, 9, 1; 1, 10, 0, 0, 0, 0, 0, 0, 0, 10, 1; ...
Programs
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Mathematica
p[x_, n_] = x^n + n*x^(n - 1) + n*x + 1; Table[CoefficientList[p[x, n], x], {n, 0, 10}] // Flatten -
Maxima
T(n, k) := ratcoef(x^n + n*x^(n - 1) + n*x + 1, x, k)$ create_list(T(n,k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Jan 25 2019 */
Extensions
Edited and offset corrected by Franck Maminirina Ramaharo, Jan 25 2019