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A147843 a(n) = -n*A010815(n). 6
0, 1, 2, 0, 0, -5, 0, -7, 0, 0, 0, 0, 12, 0, 0, 15, 0, 0, 0, 0, 0, 0, -22, 0, 0, 0, -26, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -51, 0, 0, 0, 0, 0, -57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -92, 0, 0, 0, 0, 0, 0, 0, -100, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Convolved with the partition numbers A000041 = sigma(n) prefaced with a 0 gives (0, 1, 3, 4, 7, 6, 12, 8, 15, 13,...).

Triangle A174740 convolves the partition numbers with a variant of this sequence, having row sums = A000203, sigma(n). - Gary W. Adamson, Mar 28 2010

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)

FORMULA

G.f.: -x * d eta(x)/dx (derivative)  where eta(x) = prod(n>=1, 1-x^n). - Joerg Arndt, Mar 14 2010

a(n) = Sum_{k=0..n-1} A010815(k)*sigma(n-k), where sigma(n) = A000203(n) is the number of divisors of n. - Paul D. Hanna, Jul 02 2011

EXAMPLE

a(5) = -5 = (-5) * A010815(5) = (-5) * 1.

MATHEMATICA

A010815[n_] := SeriesCoefficient[Product[1 - x^k, {k, n}], {x, 0, n}];

Table[-n*A010815[n], {n, 0, 50}] (* G. C. Greubel, Jun 13 2017 *)

CROSSREFS

Cf. A010815, A000203, A000041, A001318, A174740.

Sequence in context: A169774 A057611 A259701 * A094597 A202992 A158830

Adjacent sequences:  A147840 A147841 A147842 * A147844 A147845 A147846

KEYWORD

sign,easy,changed

AUTHOR

Gary W. Adamson, Nov 15 2008

STATUS

approved

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Last modified July 23 04:04 EDT 2017. Contains 289686 sequences.