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A113206
Triangle read by rows of generalized Catalan numbers.
1
1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 3, 5, 3, 0, 1, 1, 0, 4, 12, 14, 12, 4, 0, 1, 1, 0, 5, 22, 55, 42, 55, 22, 5, 0, 1, 1, 0, 6, 35, 140, 273, 132, 273, 140, 35, 6, 0, 1, 1, 0, 7, 51, 285, 969, 1428, 429, 1428, 969, 285, 51, 7, 0, 1, 1, 0, 8, 70, 506, 2530, 7084, 7752, 1430, 7752, 7084
OFFSET
0,7
COMMENTS
A dual to Pascal's triangle. Row n has 2n+1 entries.
FORMULA
T(n,k) = A070914(n-|n-k|-1,|n-k|+1) if 3<=k<=2n-3 . - R. J. Mathar, Feb 08 2008
EXAMPLE
.............1
...........1.0.1
.........1.0.2.0.1
.......1.0.3.5.3.0.1
....1.0.4.12.14.12.4.0.1
.1.0.5.22.55.42.55.22.5.0.1
MAPLE
A070914 := proc(n, k) binomial(n*(k+1), n)/(n*k+1) ; end proc:
A113206 := proc(n, k) if k = 2 or k = 2*n-2 then 0 ; else A070914(n-abs(n-k)-1, abs(n-k)+1) ; fi ; end proc:
for n from 0 to 10 do for k from 1 to 2*n-1 do printf("%d ", A113206(n, k)) ; od: od: # R. J. Mathar, Feb 08 2008
MATHEMATICA
A070914[n_, k_] := Binomial[n*(k + 1), n]/(n*k + 1);
A113206[n_, k_] := If[k == 2 || k == 2*n - 2, 0, A070914[n - Abs[n-k] - 1, Abs[n-k] + 1]];
Table[A113206[n, k], {n, 0, 10}, {k, 1, 2*n - 1}] // Flatten (* Jean-François Alcover, Nov 28 2017, after R. J. Mathar *)
CROSSREFS
Sequence in context: A308400 A369816 A236541 * A158800 A144024 A185249
KEYWORD
nonn,tabf,easy
AUTHOR
N. J. A. Sloane, Jan 07 2006
STATUS
approved