A159255 Irregular triangle read by rows: row n gives expansion of (1-x+x^2)*(1+x)^n.

1, -1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 3, 2, 3, 3, 1, 1, 4, 6, 5, 5, 6, 4, 1, 1, 5, 10, 11, 10, 11, 10, 5, 1, 1, 6, 15, 21, 21, 21, 21, 15, 6, 1, 1, 7, 21, 36, 42, 42, 42, 36, 21, 7, 1, 1, 8, 28, 57, 78, 84, 84, 78, 57, 28, 8, 1, 1, 9, 36, 85, 135, 162, 168, 162, 135, 85, 36, 9, 1

Offset: 0

Author

Philippe Deléham, Apr 07 2009

Keywords

• sign
• tabf

Examples

			Row n=0 : 1, -1, 1 ;
Row n=1 : 1, 0, 0, 1 ;
Row n=2 : 1, 1, 0, 1, 1 ;
Row n=3 : 1, 2, 1, 1, 2, 1 ;
Row n=4 : 1, 3, 3, 2, 3, 3, 1 ;
Row n=5 : 1, 5, 10, 11, 10, 11, 10, 5, 1;
Row n=6 : 1, 6, 15, 21, 21, 21, 21, 15, 6, 1;
...
		

Crossrefs

Cf. A000079, A014626, A024483, A050407

Programs

PARI

row(n)=Vecrev(polcoef((1 - y + y^2)/(1 - x*(1+y)) + O(x*x^n), n))
{ for(n=0, 10, print(row(n))) } \\ Andrew Howroyd, Mar 03 2023

Formula

G.f.: A(x,y) = (1 - y + y^2)/(1 - x*(1+y)). - Andrew Howroyd, Mar 03 2023