OFFSET
0,2
COMMENTS
A variant of Pascal's triangle, the first column replaced by 2 (if n > 0), the last column dropped, and then odd rows multiplied by (-1)^n.
Absolute value row sums are A000079.
FORMULA
From Franck Maminirina Ramaharo, Nov 22 2018: (Start)
T(n,k) = (-1)^n*binomial(n, k) + (-1)^n*delta(0, k) - delta(0, n), where delta is Kronecker's delta-symbol.
G.f.: (1 + 2*x*y - (1 - x - x^2)*y^2)/((1 + y)*(1 + x*y)*(1 + y + x*y)).
E.g.f.: (1 - exp(y) + exp(x*y))*exp(-(1 + x)*y). (End)
EXAMPLE
Triangle begins:
1;
-2;
2, 2;
-2, -3, -3;
2, 4, 6, 4;
-2, -5, -10, -10, -5;
2, 6, 15, 20, 15, 6;
-2, -7, -21, -35, -35, -21, -7;
2, 8, 28, 56, 70, 56, 28, 8;
-2, -9, -36, -84, -126, -126, -84, -36, -9;
2, 10, 45, 120, 210, 252, 210, 120, 45, 10;
-2, -11, -55, -165, -330, -462, -462, -330, -165, -55, -11;
2, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12;
...
MATHEMATICA
Table[CoefficientList[(-1)^n*(x + 1)^n - (-1)^n*(x^n - 1), x], {n, 0, 12}]
PROG
(Maxima) create_list((-1)^n*binomial(n, k) + (-1)^n*kron_delta(0, k) - kron_delta(0, n), n, 0, 12, k, 0, max(0, n - 1)); /* Franck Maminirina Ramaharo, Nov 21 2018 */
CROSSREFS
KEYWORD
sign,tabf,easy
AUTHOR
Roger L. Bagula, Nov 29 2009
STATUS
approved