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A168641
Triangle read by rows: T(n,k) = [x^k] p(x,n), where p(x,n) = 3*(x + 1)^n - 2*(x^n + 1) - n*(x + x^(n - 1)) for n >= 2, p(x,0) = 1, and p(x,1) = x + 1.
4
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 8, 18, 8, 1, 1, 10, 30, 30, 10, 1, 1, 12, 45, 60, 45, 12, 1, 1, 14, 63, 105, 105, 63, 14, 1, 1, 16, 84, 168, 210, 168, 84, 16, 1, 1, 18, 108, 252, 378, 378, 252, 108, 18, 1, 1, 20, 135, 360, 630, 756, 630, 360, 135, 20, 1
OFFSET
0,5
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 6, 6, 1;
1, 8, 18, 8, 1;
1, 10, 30, 30, 10, 1;
1, 12, 45, 60, 45, 12, 1;
1, 14, 63, 105, 105, 63, 14, 1;
1, 16, 84, 168, 210, 168, 84, 16, 1;
1, 18, 108, 252, 378, 378, 252, 108, 18, 1;
1, 20, 135, 360, 630, 756, 630, 360, 135, 20, 1;
...
MATHEMATICA
p[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, 3*(x + 1)^n - (x^n + 1) - (x^n + n*x^(n - 1) + n*x + 1)]];
Flatten[Table[CoefficientList[p[x, n], x], {n, 0, 10}]]
PROG
(Maxima) T(n, k) := ratcoef(if n <= 2 then (1 + x)^n else 3*(x + 1)^n - (x^n + 1) - (x^n + n*x^(n - 1) + n*x + 1), x, k);
create_list(T(n, k), n, 0, 12, k, 0, n); /* Franck Maminirina Ramaharo, Jan 02 2019 */
CROSSREFS
KEYWORD
nonn,easy,less,tabl
AUTHOR
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 02 2019
STATUS
approved