A167552 A triangle related to the a(n) formulas of the rows of the ED1 array A167546.

1, 3, -2, 5, -5, 2, 7, -7, 14, -8, 9, -6, 63, -66, 24, 11, 0, 209, -264, 308, -144, 13, 13, 559, -689, 2236, -2132, 720, 15, 35, 1281, -1255, 11640, -14980, 14064, -5760, 17, 68, 2618, -1360, 47753, -68068, 145452, -126480, 40320

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009, Nov 23 2009

Keywords

• sign
• tabl

Comments

The a(n) formulas given below correspond to the first ten rows of the ED1 array A167546.

The recurrence relations of the a(n) formulas for the left hand triangle columns, see the cross-references below, lead to the sequences A003148 and A007318.

Examples

			Row 1: a(n) = 1.
Row 2: a(n) = 3*n - 2.
Row 3: a(n) = 5*n^2 - 5*n + 2.
Row 4: a(n) = 7*n^3 - 7*n^2 + 14*n - 8.
Row 5: a(n) = 9*n^4 - 6*n^3 + 63*n^2 - 66*n + 24.
Row 6: a(n) = 11*n^5 + 0*n^4 + 209*n^3 - 264*n^2 + 308*n - 144.
Row 7: a(n) = 13*n^6 +13*n^5 +559*n^4 -689*n^3 +2236*n^2 -2132*n +720.
Row 8: a(n) = 15*n^7 + 35*n^6 + 1281*n^5 - 1255*n^4 + 11640*n^3 - 14980*n^2 + 14064*n - 5760.
Row 9: a(n) = 17*n^8 + 68*n^7 + 2618*n^6 - 1360*n^5 + 47753*n^4 - 68068*n^3 + 145452*n^2 - 126480*n + 40320.
Row 10: a(n) = 19*n^9 + 114*n^8 + 4902*n^7 + 684*n^6 + 163419*n^5 - 224694*n^4 + 1048268*n^3 - 1308264*n^2 + 1081632*n - 403200.
		

Crossrefs

A167546 is the ED1 array.

A000012, A016777, 2*A005891, A167547, A167548 and A167549 are the first sixth ED1 array rows.

A098557 and A167553 equal the first two right hand columns of this triangle.

A005408, A167554 and A167555, A168302 and A168303 equal the first five left hand columns of this triangle.

A000142 equals the row sums.

Cf. A003148 and A007318.