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

Author

Mats Granvik, Sep 02 2010

Keywords

• frac
• sign

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

Crossrefs

Cf. A001790, A046161 (denominators).

Formula

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

Extensions

Signs of terms corrected by Mats Granvik, Sep 05 2010

Corrected and edited by Mats Granvik, Oct 08 2010