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

1,3

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.

Links

Table of n, a(n) for n=1..45.

Example

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.

Sequence in context: A257257 A257251 A068555 * A221438 A327991 A193322

Adjacent sequences: A167553 A167554 A167555 * A167557 A167558 A167559

Keyword

sign,tabl

Author

Johannes W. Meijer, Nov 10 2009

Status

approved