A167591 A triangle related to the a(n) formulas of the rows of the ED4 array A167584.

1, 4, -2, 12, -8, 9, 32, -16, 120, -60, 80, 0, 952, -768, 525, 192, 160, 5664, -5008, 12396, -5670, 448, 896, 27888, -20672, 162740, -133128, 72765, 1024, 3584, 120064, -46720, 1537216, -1562464, 2557296, -1081080, 2304, 12288, 467712, 76800

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• sign
• tabl

Comments

The a(n) formulas given below correspond to the first ten rows of the ED4 array A167584.

The recurrence relations of the a(n) formulas for the left hand triangle columns, see the cross-references below, lead to the sequences A013609, A003148, A081277 and A079628.

Examples

			Row 1: a(n) = 1.
Row 2: a(n) = 4*n - 2.
Row 3: a(n) = 12*n^2 - 8*n + 9.
Row 4: a(n) = 32*n^3 - 16*n^2 + 120*n - 60.
Row 5: a(n) = 80*n^4 + 0*n^3 + 952*n^2 - 768*n + 525.
Row 6: a(n) = 192*n^5 + 160*n^4 + 5664*n^3 - 5008*n^2 + 12396*n - 5670.
Row 7: a(n) = 448*n^6 + 896*n^5 + 27888*n^4 - 20672*n^3 + 162740*n^2 - 133128*n + 72765.
Row 8: a(n) = 1024*n^7 + 3584*n^6 + 120064*n^5 - 46720*n^4 + 1537216*n^3 - 1562464*n^2 + 2557296*n - 1081080.
Row 9: a(n) = 2304*n^8 + 12288*n^7 + 467712*n^6 + 76800*n^5 + 11589216*n^4 - 12058368*n^3 + 47963568*n^2 - 38278080*n + 18243225.
Row 10: a(n) = 5120*n^9 + 38400*n^8 + 1686528*n^7 + 1540608*n^6 + 73898880*n^5 - 66179520*n^4 + 631348672*n^3 - 669559008*n^2 + 869709780*n - 344594250.
		

Crossrefs

A167584 is the ED4 array.

A000012, A016825, A167585, A167586 and A167587 equal the first five rows of the ED4 array.

A001787, A167592, A167593, A168307 and A168308 equal the first five left hand triangle columns.

A001193 equals the first right hand triangle column.

A024199 equals the row sums.

Cf. A013609, A003148, A079628 and A081277.

Extensions

Comment and formulas added by Johannes W. Meijer, Nov 23 2009