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A110771
The r-th term of the n-th row of the following triangle is C[{T(n)-T(r-1)},r] where T(n) is the n-th triangular number. 1 3 1 6 10 1 10 36 35 1 ... Sequence contains the row sums.
2
1, 4, 17, 82, 453, 2855, 20279, 159972, 1383544, 12987671, 131301747, 1420538383, 16358806638, 199606632428, 2570446661320, 34814885202341, 494470158654963, 7344794248474716, 113829232686474480
OFFSET
1,2
COMMENTS
The first term is T(n), the n-th term is 1.
EXAMPLE
For n = 4 the terms of the 4th row are C(10,1), C(9,2), C(7,3), C(4,4). 10, 36, 35, 1 and the sum is a(4) = 82.
MATHEMATICA
A110771[n_] := Plus @@ Table[Binomial[Binomial[n + 1, 2] - Binomial[r, 2], r], {r, 1, n}]; Table[A110771[i], {i, 1, 25}] (* Keith Schneider, Jul 03 2007 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Aug 12 2005
EXTENSIONS
More terms from Keith Schneider, Jul 03 2007
STATUS
approved