##
**
Multiple Binomial Transforms and Families of Integer Sequences
**

###
Jiaqiang Pan

School of Biomedical Engineering and Instrumental Science

Zhejiang University

Hangzhou 210027

China

**Abstract:**

Based on the multiple binomial transforms introduced in this
paper, the *n*-fold generating and generated sequences of a given
integer sequence can be defined and a family of this integer
sequence can be constructed. The family sets form a partition of
the set of integer sequences. Special attention is paid to the
recurrent integer sequences, which are produced by some linear and
homogeneous recurrence relations or difference equations. For the
recurrent integer sequences, a distinct rule to construct their
families is obtained based on the linear difference calculus.

**
Full version: pdf,
dvi,
ps,
latex
**

(Concerned with sequences
A000004
A000007
A000012
A000045
A000073
A001906
A039834
A093131
A115390.)

Received October 24 2009;
revised versions received March 8 2010; March 20 2010.
Published in *Journal of Integer Sequences*, March 23 2010.

Return to
**Journal of Integer Sequences home page**