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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
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.
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
KEYWORD
nonn,tabl
AUTHOR
Paul Barry, May 20 2010
STATUS
approved