A010815 convolution inverse?

N. J. A. Sloane njas at research.att.com
Tue Jun 11 23:04:06 CEST 2002

```About convolutional inverses

Normally the conv. inv. of a sequence B is a sequence A such that
A convolved with itself gives B

There are maple programs for going both ways in the transforms files
(there's a link on the EIS pages)

In the case of A010815 this was an error, and
the correct asserion is:

%I A010815
%S A010815 1,1,1,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,
%T A010815 0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%U A010815 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%V A010815 1,-1,-1,0,0,1,0,1,0,0,0,0,-1,0,0,-1,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,
%W A010815 0,0,0,0,-1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%X A010815 0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A010815 From Euler's Pentagonal Theorem: coefficient of x^n in Product (1-x^m), m=1.. infinity. Also the q-expansion of the Dedekind eta function without the q^(1/24) factor.
%C A010815 When convolved with the partion numbers A000041 gives 1, 0, 0, 0, 0, ...
...

The only other example i found in the database is A000151,
which is correct:

%I A005750 M2855
%S A005750 1,1,3,10,39,160,702,3177,14830,70678,342860,1686486,8393681,42187148,
%T A005750 213828802,1091711076,5609297942,28982708389,150496728594,
%U A005750 784952565145,4110491658233,21602884608167,113907912618599
%N A005750 Planted matched trees with n nodes.
%C A005750 When convolverd with itself gives A000151.
....

Neil Sloane

Neil J. A. Sloane
AT&T Shannon Labs, Room C233,
180 Park Avenue, Florham Park, NJ 07932-0971
Email: njas at research.att.com
Office: 973 360 8415; fax: 973 360 8178