A096797 Triangle of coefficients, read by row polynomials P_n(y), that satisfy the g.f.: A038497(x,y) = Product_{n>=1} 1/(1-x^n)^[P_n(y)/n], with P_n(0)=0 for n>=1 and P_0(0)=1.

1, 3, 1, 8, 0, 1, 16, -1, 0, 1, 34, -15, 0, 0, 1, 54, -40, 3, 0, 0, 1, 104, -119, 21, 0, 0, 0, 1, 156, -260, 88, -1, 0, 0, 0, 1, 261, -576, 305, -27, 0, 0, 0, 0, 1, 382, -1111, 850, -155, 3, 0, 0, 0, 0, 1, 615, -2167, 2167, -638, 33, 0, 0, 0, 0, 0, 1, 842, -3854, 5056, -2164, 240, -1, 0, 0, 0, 0, 0, 1

Offset

1,2

Comments

A038497 is the matrix square of partition triangle A008284. The first column forms the Moebius transform of {n*A000041(n), n>=1}. The inverse Moebius transform of each column forms the columns of triangle {n/k*A096798(n,k)}.

Links

Table of n, a(n) for n=1..78.

Example

1/A038497(x,y) =
(1-x)^y*(1-x^2)^[(3y+y^2)/2]*(1-x^3)^[(8y+y^3)/3]*(1-x^4)^[(16y-y^2+y^4)/
4]*(1-x^5)^[(34y-15y^2+y^5)/5]*...
Rows begin:
[1],
[3,1],
[8,0,1],
[16,-1,0,1],
[34,-15,0,0,1],
[54,-40,3,0,0,1],
[104,-119,21,0,0,0,1],
[156,-260,88,-1,0,0,0,1],
[261,-576,305,-27,0,0,0,0,1],
[382,-1111,850,-155,3,0,0,0,0,1],
[615,-2167,2167,-638,33,0,0,0,0,0,1],
[842,-3854,5056,-2164,240,-1,0,0,0,0,0,1],
[1312,-6916,11089,-6409,1183,-39,0,0,0,0,0,0,1],
[1782,-11649,23037,-17241,4704,-343,3,0,0,0,0,0,0,1],...

Crossrefs

Cf. A038497, A008284, A096798.

Sequence in context: A285020 A165781 A152095 * A084246 A141252 A276168

Adjacent sequences: A096794 A096795 A096796 * A096798 A096799 A096800

Keyword

sign,tabl

Author

Paul D. Hanna, Jul 13 2004

Status

approved