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Numerator of a(n)/2^A005187(n-1), the n-th row sums of A096651^(1/2), with a(0)=1.
1

%I #3 Mar 30 2012 18:36:40

%S 1,1,3,15,41,387,1017,4715,11917,220323,517545,2403313,6436023,

%T 58028007,53008869

%N Numerator of a(n)/2^A005187(n-1), the n-th row sums of A096651^(1/2), with a(0)=1.

%C The denominators are 2^A005187(n-1) (for n>0), where A005187(n) is the number of 1's in binary expansion of 2n. Can the row sums of A096651^(1/2) be said to define the (1/2)-dimensional partitions of n?

%e Sequence begins: {1,1,3/2,15/8,41/16,387/128,1017/256,...}.

%e Formed from the row sums of triangular matrix A096651^(1/2), which begins:

%e {1},

%e {0,1},

%e {0,1/2,1},

%e {0,3/8,1/2,1},

%e {0,3/16,7/8,1/2,1},

%e {0,27/128,-1/16,11/8,1/2,1},

%e {0,35/256,99/128,-5/16,15/8,1/2,1},

%e {0,103/1024,-229/256,267/128,-9/16,19/8,1/2,1},

%e {0,-129/2048,7011/1024,-2349/256,595/128,-13/16,23/8,1/2,1},...

%e The denominator of each element at column n, row k, is A005187(n-k).

%Y Cf. A096651, A096743, A005187.

%K more,nonn

%O 0,3

%A _Paul D. Hanna_, Jul 06 2004