A167556 A triangle related to the GF(z) formulas of the rows of the ED1 array A167546.

1, 1, 2, 2, 6, 2, 6, 24, 4, 8, 24, 120, 0, 48, 24, 120, 720, -120, 384, 72, 144, 720, 5040, -1680, 3696, -432, 1296, 720, 5040, 40320, -20160, 40320, -15840, 17280, 2880, 5760, 40320, 362880, -241920, 483840, -311040, 288000, -46080, 69120, 40320

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• sign
• tabl

Comments

The GF(z) formulas given below correspond to the first ten rows of the ED1 array A167546. The polynomials in their numerators lead to the triangle given above.

Examples

			Row 1: GF(z) = 1/(1-z).
Row 2: GF(z) = (1 + 2*z)/(1-z)^2.
Row 3: GF(z) = (2 + 6*z + 2*z^2)/(1-z)^3.
Row 4: GF(z) = (6 + 24*z + 4*z^2 + 8*z^3)/(1-z)^4.
Row 5: GF(z) = (24 + 120*z + 0*z^2 + 48*z^3 + 24*z^4)/(1-z)^5.
Row 6: GF(z) = (120 + 720*z - 120*z^2 + 384*z^3 + 72*z^4 + 144*z^5)/ (1-z)^6.
Row 7: GF(z) = (720 + 5040*z - 1680*z^2 + 3696*z^3 - 432*z^4 + 1296*z^5 + 720*z^6)/(1-z)^7.
Row 8: GF(z) = (5040 + 40320*z - 20160*z^2 + 40320*z^3 - 15840*z^4 + 17280*z^5 + 2880*z^6 + 5760*z^7)/(1-z)^8.
Row 9: GF(z) = (40320 +362880*z -241920*z^2 + 483840*z^3 - 311040*z^4 + 288000*z^5 - 46080*z^6 + 69120*z^7 + 40320*z^8)/(1-z)^9.
Row 10: GF(z) = (362880 +3628800*z -3024000*z^2 +6289920*z^3 -5495040*z^4 + 5276160*z^5 - 2131200*z^6 + 1382400*z^7 + 201600*z^8 + 403200*z^9)/(1-z)^10;
		

Crossrefs

A167546 is the ED1 array.

A000142, A000142 (n=>2) and 120*A062148 (with three extra terms at the beginning of the sequence) equal the first three left hand triangle columns.

A098557(n) and A098557(n)*A064455(n) equal the first two right hand triangle columns.

A007680 equals the row sums.