|
| |
|
|
A193451
|
|
Triangle of a binomial convolution sum related to Jacobsthal numbers.
|
|
2
|
|
|
|
0, 0, 1, 0, 3, 3, 0, 5, 8, 2, 0, 7, 17, 14, 6, 0, 9, 30, 39, 24, 3, 0, 11, 47, 83, 75, 33, 9, 0, 13, 68, 152, 184, 126, 48, 4, 0, 15, 93, 252, 384, 354, 198, 60, 12, 0, 17, 122, 389, 716, 830, 620, 290, 80, 5, 0, 19, 155, 569, 1229, 1718, 1610, 1010, 410, 95, 15
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
COMMENTS
|
Row sum is A193449(n) = n*A001045(n+1).
|
|
|
LINKS
|
Table of n, a(n) for n=0..65.
|
|
|
FORMULA
|
T(n,k)= sum( (-1)^(j+k)*(j+k)*C(n-k+j,j), j=0..k).
|
|
|
EXAMPLE
|
Triangle starts:
0;
0, 1;
0, 3, 3;
0, 5, 8, 2;
0, 7, 17, 14, 6;
0, 9, 30, 39, 24, 3;
...
|
|
|
PROG
|
(PARI) T(n, k)= sum(j=0, k, (-1)^(j+k)*(j+k)*binomial(n-k+j, j)); \\ Michel Marcus, Jun 04 2014
|
|
|
CROSSREFS
|
Cf. A193449, A193450, A001045.
Sequence in context: A353327 A072689 A021972 * A335809 A322215 A244492
Adjacent sequences: A193448 A193449 A193450 * A193452 A193453 A193454
|
|
|
KEYWORD
|
nonn,easy,tabl
|
|
|
AUTHOR
|
Olivier Gérard, Jul 26 2011
|
|
|
STATUS
|
approved
|
| |
|
|
