Edwin said: Thinking of John McCarthy's suggestion, I just submitted the following sequence to the OEIS 1, 3, 6, 11, 18, 28, 42, 61, 86, 119, 162, 217, 287, 375 The nth term is the number of subsets S of {1,2,...,n} which contain a number that is greater than the sum of the other numbers in S. Perhaps someone can find a nice formula for the nth term. Me: Consider the sequence %I A000009 M0281 N0100 %S A000009 1,1,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64,76,89,104,122,142, %T A000009 165,192,222,256,296,340,390,448,512,585,668,760,864,982,1113,1260, %U A000009 1426,1610,1816,2048,2304,2590,2910,3264,3658,4097,4582,5120,5718 %N A000009 Expansion of Product (1 + x^m), m=1..inf; number of partitions of n into distinct parts; number of partitions of n into odd parts. ... Take partial sums: %I A036469 %S A036469 0,1,2,3,5,7,10,14,19,25,33,43,55,70,88,110,137,169,207,253,307,371, %T A036469 447,536,640,762,904,1069,1261,1483,1739,2035,2375,2765,3213,3725, %U A036469 4310,4978,5738,6602,7584,8697,9957,11383,12993,14809,16857,19161 %N A036469 Partial sums of A000009 (partitions into distinct parts). ... Take partial sums again: 0, 1, 3, 6, 11, 18, 28, 42, 61, 86, 119, 162, 217, 287, 375, 485, 622, 791, 998, 1251, 1558, 1929, ... (Thanks to Superseeker). Proof? NJAS