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

0,1

Links

Table of n, a(n) for n=0..90.

Example

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;
  ...

Mathematica

p[x_, n_] = x^n + n*x^(n - 1) + n*x + 1;
Table[CoefficientList[p[x, n], x], {n, 0, 10}] // Flatten

Prog

(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 */

Crossrefs

Row sums: A005843.

Cf. A144394.

Sequence in context: A350189 A289778 A277523 * A351112 A089400 A239209

Adjacent sequences: A144390 A144391 A144392 * A144394 A144395 A144396

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Gary W. Adamson, Oct 02 2008

Extensions

Edited and offset corrected by Franck Maminirina Ramaharo, Jan 25 2019

Status

approved