Definition
If two integer sequences
and
are related by[1]

or, in terms of generating functions
and
,
then
is said to be the Euler transform of
.
Combinatorial interpretation
If
is a nonnegative integer sequence with Euler transform
then
is the number of weakly increasing sequences of pairs
such that
and
for all
.
For example, the third part of the Euler transform of {1,2,4,8,...} is A034691(3) = 7, corresponding to the following 7 sequences of pairs.







Notes
- ↑ Sloane and Plouffe 1995, pp. 20-21.
References
- Sloane, N. J. A. and Plouffe, S., The Encyclopedia of Integer Sequences, San Diego, CA, Academic Press, pp. 20-21, 1995.
External links
- Eric W. Weisstein, Euler Transform, from MathWorld — A Wolfram Web Resource..