A270250 Triangle read by rows: coefficients of the polynomial (Sum_{i=0..k} (Product_{j=0..i} (x+j)))/(x*(x+2)).

1, 2, 1, 5, 5, 1, 17, 24, 9, 1, 77, 131, 68, 14, 1, 437, 833, 529, 151, 20, 1, 2957, 6107, 4458, 1571, 290, 27, 1, 23117, 50819, 41164, 16860, 3870, 505, 35, 1, 204557, 473387, 416230, 191167, 51379, 8387, 819, 44, 1, 2018957, 4880507, 4589458, 2309303, 700776, 134716, 16541, 1258, 54, 1

Offset: 1

Author

Michel Marcus, Mar 14 2016

Keywords

• nonn
• tabl

Comments

The lines offset is 1, but the columns offset is 0.

Examples

			First rows of this triangle:
   1;
   2,   1;
   5,   5,   1;
  17,  24,   9,   1;
  77, 131,  68,  14,   1;
  ...
		

Links

• Lajos Hajdu, Shanta Laishram, Szabolcs Tengely, Power values of sums of products of consecutive integers, Acta Arithmetica 172 (2016), 333-349.

Crossrefs

Cf. A007489 (values of polynomial when x=2), A014288 (first column).

Programs

PARI

row(n) = Vecrev(sum(i=0, n, prod(j=0, i, x+j))/(x*(x+2)));