0,3

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^(3/2) be said to define the (3/2)-dimensional partitions of n?

a(n)/2^A005187(n-1) = Sum_{k=0..n} A096651(n, k)*A096742(k)/2^A005187(k-1).

Sequence begins: {1,1,5/2,35/8,135/16,1755/128,6303/256,...}.

Formed from the row sums of triangular matrix A096651^(3/2), which begins:

{1},

{0,1},

{0,3/2,1},

{0,15/8,3/2,1},

{0,41/16,27/8,3/2,1},

{0,387/128,53/16,39/8,3/2,1},

{0,1017/256,987/128,65/16,51/8,3/2,1},

{0,4715/1024,753/256,2067/128,77/16,63/8,3/2,1},

{0,11917/2048,29983/1024,-4503/256,3819/128,89/16,75/8,3/2,1},...

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

Cf. A096651, A096742, A005187.

Sequence in context: A161199 A111877 A053126 this_sequence A026697 A000910 A005562

Adjacent sequences: A096740 A096741 A096742 this_sequence A096744 A096745 A096746

more,nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2004