A180403 Numerator in Moebius transform of A001790/A046161.

1, -1, -5, -3, -93, 95, -793, -211, -5853, 27003, -215955, 57459, -3518265, 3602027, 16811055, -4362627, -1846943453, 293601363, -14911085359, 4487888279, 144251733709, 245294787521, -1936010885087, 228009405371, -11179552565305, 63485965327535, -48562641580527

Offset

1,3

Comments

Consider a lower triangular matrix T(n,k) defined by T(n,1)=A001790/A046161, k>1: T(n,k) = (Sum_{i=1..k-1} T(n-i,k-1)) - (Sum_{i=1..k-1} T(n-i,k)). The first column in the matrix inverse of T(n,k) will have the fraction A180403/A046161 in its first column.

The sequence considers the Moebius transform 1, -1/2, -5/8, -3/16, -93/128, ... of the sequence A001790(n-1)/A046161(n-1), i.e., assigning offset 1 to A001790 and A046161. - R. J. Mathar, Apr 22 2011

Links

Table of n, a(n) for n=1..27.

Formula

Lambert series: Sum_{n >= 1} (A180403(n)/A046161(n))*x^n/(1-x^n) = x/sqrt(1-x). - Mats Granvik, Sep 07 2010

Crossrefs

Cf. A001790, A046161 (denominators).

Sequence in context: A370551 A350213 A255599 * A343582 A267512 A230389

Adjacent sequences: A180400 A180401 A180402 * A180404 A180405 A180406

Keyword

frac,sign

Author

Mats Granvik, Sep 02 2010

Extensions

Signs of terms corrected by Mats Granvik, Sep 05 2010

Corrected and edited by Mats Granvik, Oct 08 2010

Status

approved