Inversion of Generating Functions using Determinants
Kwang-Wu Chen
Department of Mathematics and Computer Science Education
Taipei Municipal University of Education
No. 1, Ai-Kuo West Road
Taipei 100
Taiwan
Republic of China
Abstract:
In this note, we prove that the coefficients of an ordinary generating function
can be deduced from some determinant formula about the coefficients in
the reciprocal of the ordinary generating function. We use this result
to obtain determinant identities for some well-known numbers.
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(Concerned with sequences
A000047
A000182
A001318
A001469
A008275 and
A008277
.)
Received October 10 2007;
revised version received December 31 2007.
Published in Journal of Integer Sequences, December 31 2007.
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