|Journal of Integer Sequences, Vol. 6 (2003), Article 03.3.3|
Abstract: The integer sequences with first term comprise a group under convolution, namely, the Appell group, and the lower triangular infinite integer matrices with all diagonal entries comprise a group under matrix multiplication. If and then The groups and and various subgroups are discussed. These include the group of matrices whose columns are identical except for initial zeros, and also the group of matrices in which the odd-numbered columns are identical except for initial zeros and the same is true for even-numbered columns. Conditions are determined for the product of two matrices in to be in Conditions are also determined for two matrices in to commute.
(Concerned with sequences A000045 A000108 A000142 A000201 A000204 A000741 A000984 A002530 A047749 A077049 A077050 A077605 A077606 .)
Received November 13, 2002; revised version received January 28, 2002; September 2, 2003. Published in Journal of Integer Sequences September 8, 2003.