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A270250
Triangle read by rows: coefficients of the polynomial (Sum_{i=0..k} (Product_{j=0..i} (x+j)))/(x*(x+2)).
0
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
1,2
COMMENTS
The lines offset is 1, but the columns offset is 0.
LINKS
Lajos Hajdu, Shanta Laishram, Szabolcs Tengely, Power values of sums of products of consecutive integers, Acta Arithmetica 172 (2016), 333-349.
EXAMPLE
First rows of this triangle:
1;
2, 1;
5, 5, 1;
17, 24, 9, 1;
77, 131, 68, 14, 1;
...
PROG
(PARI) row(n) = Vecrev(sum(i=0, n, prod(j=0, i, x+j))/(x*(x+2)));
CROSSREFS
Cf. A007489 (values of polynomial when x=2), A014288 (first column).
Sequence in context: A137597 A059340 A248727 * A204119 A046757 A248905
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, Mar 14 2016
STATUS
approved