A096742 Numerator of a(n)/2^A005187(n-1), the n-th row sums of A096651^(1/2), with a(0)=1.

1, 1, 3, 15, 41, 387, 1017, 4715, 11917, 220323, 517545, 2403313, 6436023, 58028007, 53008869

Offset

0,3

Comments

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?

Links

Table of n, a(n) for n=0..14.

Example

Sequence begins: {1,1,3/2,15/8,41/16,387/128,1017/256,...}.
Formed from the row sums of triangular matrix A096651^(1/2), which begins:
{1},
{0,1},
{0,1/2,1},
{0,3/8,1/2,1},
{0,3/16,7/8,1/2,1},
{0,27/128,-1/16,11/8,1/2,1},
{0,35/256,99/128,-5/16,15/8,1/2,1},
{0,103/1024,-229/256,267/128,-9/16,19/8,1/2,1},
{0,-129/2048,7011/1024,-2349/256,595/128,-13/16,23/8,1/2,1},...
The denominator of each element at column n, row k, is A005187(n-k).

Crossrefs

Cf. A096651, A096743, A005187.

Sequence in context: A299608 A249835 A295938 * A012256 A012222 A069267

Adjacent sequences: A096739 A096740 A096741 * A096743 A096744 A096745

Keyword

more,nonn

Author

Paul D. Hanna, Jul 06 2004

Status

approved