A167580 A triangle related to the a(n) formulas of the rows of the ED3 array A167572.

1, 6, -1, 20, 0, 3, 56, 28, 98, -15, 144, 192, 1080, -48, 105, 352, 880, 7568, 2024, 6534, -945, 832, 3328, 40976, 31616, 132444, -8112, 10395, 1920, 11200, 187488, 274480, 1593960, 286900, 972162, -135135, 4352, 34816, 761600, 1784320, 13962848

Offset

1,2

Comments

The a(n) formulas given below correspond to the first ten rows of the ED3 array A167572.

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.

Links

Table of n, a(n) for n=1..41.

Example

Row 1: a(n) = 1.
Row 2: a(n) = 6*n - 1.
Row 3: a(n) = 20*n^2 + 0*n + 3.
Row 4: a(n) = 56*n^3 + 28*n^2 + 98*n - 15.
Row 5: a(n) = 144*n^4 + 192*n^3 + 1080*n^2 - 48*n + 105.
Row 6: a(n) = 352*n^5 + 880*n^4 + 7568*n^3 + 2024*n^2 + 6534*n - 945.
Row 7: a(n) = 832*n^6 + 3328*n^5 + 40976*n^4 + 31616*n^3 + 132444*n^2 - 8112*n + 10395.
Row 8: a(n) = 1920*n^7 + 11200*n^6 + 187488*n^5 + 274480*n^4 + 1593960*n^3 + 286900*n^2 + 972162*n - 135135.
Row 9: a(n) = 4352*n^8 + 34816*n^7 + 761600*n^6 + 1784320*n^5 + 13962848*n^4 + 7874944*n^3 + 29641200*n^2 - 2080800*n + 2027025.
Row 10: a(n) = 9728*n^9 + 102144*n^8 + 2830848*n^7 + 9645312*n^6 + 98382912*n^5 + 106720416*n^4 + 522283552*n^3 + 69265488*n^2 + 255468870*n - 34459425.

Crossrefs

A167572 is the ED3 array.

A000012, A016969, A167573, A167574 and A167575 equal the first five rows of the ED3 array.

A014480, A167581, A167582, A168305 and A168306 equal the first five left hand triangle columns.

A001147 equals the first right hand triangle column.

A167576 equals the row sums.

Cf. A013609, A003148, A079628 and A081277.

Sequence in context: A019430 A064083 A152249 * A080213 A200091 A180733

Adjacent sequences: A167577 A167578 A167579 * A167581 A167582 A167583

Keyword

sign,tabl

Author

Johannes W. Meijer, Nov 10 2009

Extensions

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

Status

approved