login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A106187
Sequence array for central binomial numbers A000984.
3
1, 2, 1, 6, 2, 1, 20, 6, 2, 1, 70, 20, 6, 2, 1, 252, 70, 20, 6, 2, 1, 924, 252, 70, 20, 6, 2, 1, 3432, 924, 252, 70, 20, 6, 2, 1, 12870, 3432, 924, 252, 70, 20, 6, 2, 1, 48620, 12870, 3432, 924, 252, 70, 20, 6, 2, 1, 184756, 48620, 12870, 3432, 924, 252, 70, 20, 6, 2, 1
OFFSET
0,2
FORMULA
T(n, k) = binomial(2*(n-k), n-k).
Riordan array (1/sqrt(1-4x), x).
EXAMPLE
Triangle begins:
1;
2, 1;
6, 2, 1;
20, 6, 2, 1;
70, 20, 6, 2, 1;
252, 70, 20, 6, 2, 1;
...
The matrix inverse starts:
1;
-2,1;
-2,-2,1;
-4,-2,-2,1;
-10,-4,-2,-2,1;
-28,-10,-4,-2,-2,1;
-84,-28,-10,-4,-2,-2,1;
-264,-84,-28,-10,-4,-2,-2,1;
apparently related to A002420. - R. J. Mathar, Apr 08 2013
MAPLE
A106187 := proc(n, k)
binomial(2*(n-k), n-k) ;
end proc: # R. J. Mathar, Apr 08 2013
MATHEMATICA
T[n_, k_] := (((2*n - 2*k)!)/((n - k)!)^2); Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Detlef Meya, Aug 11 2024 *)
CROSSREFS
Row sums are A006134.
Antidiagonal sums are A106188.
Cf. A000984.
Sequence in context: A101024 A124730 A114283 * A110135 A114423 A335109
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Apr 24 2005
STATUS
approved