A171414 Triangle read by rows (n >= 1): T(n,k) = [x^k] p(x,n), where p(x,n) = ((x^n - 1)/(x - 1))^floor(n/2) if n is odd, and p(x,n) = ((x^n - 1)/(x - 1))*p(x,n-1) otherwise.

1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 1, 3, 6, 10, 15, 19, 21, 21, 19, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 28, 33, 36, 37, 36, 33, 28, 21, 15, 10, 6, 3, 1, 1, 4, 10, 20, 35, 56, 84, 117, 152, 186, 216, 239, 252, 252, 239, 216, 186, 152, 117, 84, 56, 35, 20, 10, 4, 1

Offset

1,8

Links

Table of n, a(n) for n=1..80.

Example

Triangle begins:
  1;
  1, 1;
  1, 1, 1;
  1, 2, 3,  3,  2,  1;
  1, 2, 3,  4,  5,  4,  3,  2,  1;
  1, 3, 6, 10, 15, 19, 21, 21, 19, 15, 10,  6,  3,  1;
  1, 3, 6, 10, 15, 21, 28, 33, 36, 37, 36, 33, 28, 21, 15, 10, 6, 3, 1;
  ...

Mathematica

p[x_, n_] := p[x, n] = If[Mod[n, 2] == 0, Sum[x^i, {i, 0, n - 1}]*p[x, n - 1], (Sum[x^i, {i, 0, n - 1}])^Floor[n/2]]
Flatten[Table[CoefficientList[p[x, n], x], {n, 1, 12}]]

Prog

(Maxima)
p(x, n) := if mod(n, 2) = 0 then ((x^n - 1)/(x - 1))*p(x, n - 1) else ((x^n - 1)/(x - 1))^floor(n/2)$
T(n, k) := ratcoef(p(x, n), x, k)$
create_list(T(n, k), n, 1, 10, k, 0, hipow(fullratsimp(p(x, n)), x));
/* Franck Maminirina Ramaharo, Jan 13 2019 */

Crossrefs

Cf. A008406, A171412.

Sequence in context: A274885 A287732 A334223 * A270921 A038529 A176259

Adjacent sequences: A171411 A171412 A171413 * A171415 A171416 A171417

Keyword

nonn,easy,tabf

Author

Roger L. Bagula, Dec 08 2009

Extensions

Edited by Franck Maminirina Ramaharo, Jan 13 2019

Status

approved