A178116 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, 4, 0, 7, 0, 1, 0, 22, 0, 13, 0, 1, 36, 0, 85, 0, 22, 0, 1, 0, 300, 0, 241, 0, 34, 0, 1, 576, 0, 1660, 0, 593, 0, 50, 0, 1, 0, 6576, 0, 6480, 0, 1273, 0, 70, 0, 1, 14400, 0, 48076, 0, 21305, 0, 2523, 0, 95, 0, 1, 0, 211680, 0, 242476, 0, 59495, 0, 4623

Offset

0,8

Comments

First column is n!^2 (A001044) aerated. Inverse is A178117.

Links

Table of n, a(n) for n=0..73.

Example

Triangle begins
1,
0, 1,
1, 0, 1,
0, 3, 0, 1,
4, 0, 7, 0, 1,
0, 22, 0, 13, 0, 1,
36, 0, 85, 0, 22, 0, 1,
0, 300, 0, 241, 0, 34, 0, 1,
576, 0, 1660, 0, 593, 0, 50, 0, 1,
0, 6576, 0, 6480, 0, 1273, 0, 70, 0, 1,
14400, 0, 48076, 0, 21305, 0, 2523, 0, 95, 0, 1
Production matrix is 0, 1,
1, 0, 1,
0, 2, 0, 1,
1, 0, 4, 0, 1,
0, 4, 0, 6, 0, 1,
1, 0, 11, 0, 9, 0, 1,
0, 6, 0, 24, 0, 12, 0, 1,
1, 0, 22, 0, 46, 0, 16, 0, 1,
0, 8, 0, 62, 0, 80, 0, 20, 0, 1
Production matrix of inverse 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: A273083 A307451 A247629 * A238709 A245120 A226912

Adjacent sequences: A178113 A178114 A178115 * A178117 A178118 A178119

Keyword

nonn,tabl

Author

Paul Barry, May 20 2010

Status

approved