A096743 - OEIS

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A096743

Numerator of a(n)/2^A005187(n-1), the n-th row sums of A096651^(3/2), with a(0)=1.

1, 1, 5, 35, 135, 1755, 6303, 39815, 132675, 3322515, 10561455, 64566253, 199681945, 2391238415, 7233344915 (list; graph; refs; listen; history; internal format)

	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^(3/2) be said to define the (3/2)-dimensional partitions of n?`
	FORMULA	`a(n)/2^A005187(n-1) = Sum_{k=0..n} A096651(n, k)*A096742(k)/2^A005187(k-1).`
	EXAMPLE	`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).`
	CROSSREFS	`Cf. A096651, A096742, A005187.` `Sequence in context: A111877 A179337 A053126 * A026697 A000910 A005562` `Adjacent sequences: A096740 A096741 A096742 * A096744 A096745 A096746`
	KEYWORD	`more,nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Jul 06 2004`

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Last modified February 16 10:53 EST 2012. Contains 205904 sequences.