A147843 a(n) = -n*A010815(n).

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

Offset: 0

Author

Gary W. Adamson, Nov 15 2008

Keywords

• sign
• easy

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

PARI

a(n) = -n * if(issquare(24*n + 1, &n), kronecker(12, n)); \\ Amiram Eldar, Jan 19 2024 after  Michael Somos at A010815

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 sum of divisors of n. - Paul D. Hanna, Jul 02 2011