A178117 Inverse of coefficient array for polynomials P(n,x)=x*P(n-1,x)+floor(n^2/4)*P(n-2,x), P(0,x)=1,P(1,x)=x.

1, 0, 1, -1, 0, 1, 0, -3, 0, 1, 3, 0, -7, 0, 1, 0, 17, 0, -13, 0, 1, -17, 0, 69, 0, -22, 0, 1, 0, -155, 0, 201, 0, -34, 0, 1, 155, 0, -959, 0, 507, 0, -50, 0, 1, 0, 2073, 0, -4001, 0, 1107, 0, -70, 0, 1, -2073, 0, 18077, 0, -13964, 0, 2227, 0, -95, 0, 1, 0, -38227, 0, 101861, 0

Offset

0,8

Comments

First column is the aerated Genocchi numbers A001469. Inverse is A178116.

Links

Table of n, a(n) for n=0..70.

Example

Triangle begins
1,
0, 1,
-1, 0, 1,
0, -3, 0, 1,
3, 0, -7, 0, 1,
0, 17, 0, -13, 0, 1,
-17, 0, 69, 0, -22, 0, 1,
0, -155, 0, 201, 0, -34, 0, 1,
155, 0, -959, 0, 507, 0, -50, 0, 1,
0, 2073, 0, -4001, 0, 1107, 0, -70, 0, 1,
-2073, 0, 18077, 0, -13964, 0, 2227, 0, -95, 0, 1
Production matrix is
0, 1,
-1, 0, 1,
0, -2, 0, 1,
0, 0, -4, 0, 1,
0, 0, 0, -6, 0, 1,
0, 0, 0, 0, -9, 0, 1,
0, 0, 0, 0, 0, -12, 0, 1,
0, 0, 0, 0, 0, 0, -16, 0, 1,
0, 0, 0, 0, 0, 0, 0, -20, 0, 1

Crossrefs

Sequence in context: A066325 A099174 A137297 * A095710 A216416 A291960

Adjacent sequences: A178114 A178115 A178116 * A178118 A178119 A178120

Keyword

sign,tabl

Author

Paul Barry, May 20 2010

Status

approved