A167565 A triangle related to the a(n) formulas for the rows of the ED2 array A167560.

1, 2, 0, 3, 1, 2, 4, 4, 16, 0, 5, 10, 67, 14, 24, 6, 20, 202, 124, 368, 0, 7, 35, 497, 601, 2736, 444, 720, 8, 56, 1064, 2120, 13712, 6464, 16896, 0, 9, 84, 2058, 6096, 53121, 48876, 186732, 25584, 40320, 10, 120, 3684, 15168, 171258, 257640, 1350296

Offset: 1

Author

Johannes W. Meijer, Nov 10 2009

Keywords

• nonn
• tabl

Comments

The a(n) formulas given below correspond to the first ten rows of the ED2 array A167560.

The recurrence relations for 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) = 2*n + 0.
Row 3: a(n) = 3*n^2 + 1*n + 2.
Row 4: a(n) = 4*n^3 + 4*n^2 + 16*n + 0.
Row 5: a(n) = 5*n^4 + 10*n^3 + 67*n^2 + 14*n + 24.
Row 6: a(n) = 6*n^5 + 20*n^4 + 202*n^3 + 124*n^2 + 368*n + 0.
Row 7: a(n) = 7*n^6 + 35*n^5 + 497*n^4 + 601*n^3 + 2736*n^2 + 444*n + 720.
Row 8: a(n) = 8*n^7 + 56*n^6 + 1064*n^5 + 2120*n^4 + 13712*n^3 + 6464*n^2 + 16896*n + 0.
Row 9: a(n) = 9*n^8 + 84*n^7 + 2058*n^6 + 6096*n^5 + 53121*n^4 + 48876*n^3 + 186732*n^2 + 25584*n + 40320.
Row 10: a(n) = 10*n^9 + 120*n^8 + 3684*n^7 + 15168*n^6 + 171258*n^5 + 257640*n^4 + 1350296*n^3 + 533472*n^2 + 1297152*n + 0.
		

Crossrefs

A167560 is the ED2 array.

A000012, A005843 (n=>1), 2*A104249 (n=>1), A167561, A167562 and A167563 equal the first sixth rows of the array.

A005359 equals the first right hand triangle column.

A000027, A000292, A167566, A167567 and A168304 equal the first five left hand triangle columns.

A000142 equals the row sums.

Cf. A003148 and A007318.

Extensions

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