Geodesic
Inversion of generating functions using determinants
Journal of integer sequences, Tome 10 (2007) no. 10
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.
Classification : 11C20, 11B68
Keywords: generating function inversion, determinant formulas, Toeplitz matrix, Bernoulli numbers of order m, Stirling numbers 
@article{JIS_2007__10_10_a0,
     author = {Chen,  Kwang-Wu},
     title = {Inversion of generating functions using determinants},
     journal = {Journal of integer sequences},
     year = {2007},
     volume = {10},
     number = {10},
     zbl = {1174.11362},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2007__10_10_a0/}
}
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Chen,  Kwang-Wu. Inversion of generating functions using determinants. Journal of integer sequences, Tome 10 (2007) no. 10. http://geodesic.mathdoc.fr/item/JIS_2007__10_10_a0/