A171414 - OEIS

%I #9 Jan 13 2019 12:07:31

%S 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,

%T 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,

%U 20,35,56,84,117,152,186,216,239,252,252,239,216,186,152,117,84,56,35,20,10,4,1

%N 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.

%e Triangle begins:

%e   1;

%e   1, 1;

%e   1, 1, 1;

%e   1, 2, 3,  3,  2,  1;

%e   1, 2, 3,  4,  5,  4,  3,  2,  1;

%e   1, 3, 6, 10, 15, 19, 21, 21, 19, 15, 10,  6,  3,  1;

%e   1, 3, 6, 10, 15, 21, 28, 33, 36, 37, 36, 33, 28, 21, 15, 10, 6, 3, 1;

%e   ...

%t 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]]

%t Flatten[Table[CoefficientList[p[x, n], x], {n, 1, 12}]]

%o (Maxima)

%o 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)$

%o T(n, k) := ratcoef(p(x, n), x, k)$

%o create_list(T(n, k), n, 1, 10, k, 0, hipow(fullratsimp(p(x, n)), x));

%o /* _Franck Maminirina Ramaharo_, Jan 13 2019 */

%Y Cf. A008406, A171412.

%K nonn,easy,tabf

%O 1,8

%A _Roger L. Bagula_, Dec 08 2009

%E Edited by _Franck Maminirina Ramaharo_, Jan 13 2019