A167431 Riordan array (1-4x+4x^2, x(1-2x)).

1, -4, 1, 4, -6, 1, 0, 12, -8, 1, 0, -8, 24, -10, 1, 0, 0, -32, 40, -12, 1, 0, 0, 16, -80, 60, -14, 1, 0, 0, 0, 80, -160, 84, -16, 1, 0, 0, 0, -32, 240, -280, 112, -18, 1, 0, 0, 0, 0, -192, 560, -448, 144, -20, 1, 0, 0, 0, 0, 64, -672, 1120, -672, 180, -22, 1

Offset

0,2

Comments

Row sums are A167433. Diagonal sums are A167434. Central coefficients are (-1)^n*A001788(n+1).

Inverse is A167432.

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k)=T(n-1,k-1)-2*T(n-2,k-1), T(0,0)=1, T(1,0)=-4, T(2,0)=4, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Nov 13 2013

Example

Triangle begins
1,
-4, 1,
4, -6, 1,
0, 12, -8, 1,
0, -8, 24, -10, 1,
0, 0, -32, 40, -12, 1,
0, 0, 16, -80, 60, -14, 1,
0, 0, 0, 80, -160, 84, -16, 1,
0, 0, 0, -32, 240, -280, 112, -18, 1,
0, 0, 0, 0, -192, 560, -448, 144, -20, 1,
0, 0, 0, 0, 64, -672, 1120, -672, 180, -22, 1

Crossrefs

Sequence in context: A081773 A324836 A302151 * A205848 A297701 A110361

Adjacent sequences: A167428 A167429 A167430 * A167432 A167433 A167434

Keyword

easy,sign,tabl

Author

Paul Barry, Nov 03 2009

Status

approved