%I A110771
%S A110771 1,4,17,82,453,2855,20279,159972,1383544,12987671,131301747,
%T A110771 1420538383,16358806638,199606632428,2570446661320,34814885202341,
%U A110771 494470158654963,7344794248474716,113829232686474480
%N 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.
%C A110771 The first term is T(n), the n-th term is 1.
%e A110771 For n = 4 the terms of the 4-th 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.
%t A110771 A110771[n_] := Plus @@ Table[Binomial[Binomial[n + 1, 2] - Binomial[r, 
               2], r], {r, 1, n}]; Table[A110771[i], {i, 1, 25}]
%Y A110771 Cf. A110768, A110769, A110770.
%Y A110771 Sequence in context: A151250 A121545 A078845 this_sequence A082028 A052315 
               A093904
%Y A110771 Adjacent sequences: A110768 A110769 A110770 this_sequence A110772 A110773 
               A110774
%K A110771 easy,nonn
%O A110771 1,2
%A A110771 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 12 2005
%E A110771 More terms and Mathematica program from Keith Schneider, Jul 03 2007