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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
OFFSET
0,5
COMMENTS
Row sum is A193449(n) = n*A001045(n+1).
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
KEYWORD
nonn,easy,tabl
AUTHOR
Olivier Gérard, Jul 26 2011
STATUS
approved