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The Gould and Hsu matrix inversion formula defines lower triangular matrices 
and 
from a sequence 
of complex numbers by
 |
and
 |
where the product over an empty set is 1. Then 
and 
are matrix inverses (Bhatnagar 1995, pp. 15-16
and 50-51). The Krattenthaler
matrix inversion formula is a generalization of this result.
Extensions." PhD thesis. Columbus, OH: Ohio State
University, 1995. https://web.archive.org/web/20040218044148/http://www.math.ohio-state.edu/~milne/papers/Gaurav.whole.thesis.7.4.ps.Carlitz,
L. "Some Inverse Relations." Duke Math. J. 40, 893-901, 1972.Chu,
W. C. and Hsu, L. C. "Some New Applications of Gould-Hsu Inversions."
J. Combin. Inform. System Sci. 14, 1-4, 1989.Gessel, I.
and Stanton, D. "Application of 
-Lagrange Inversion to Basic Hypergeometric Series." Trans.
Amer. Math. Soc. 277, 173-201, 1983.Gould, H. W. and
Hsu, L. C. "Some New Inverse Series Relations." Duke Math. J. 40,
885-891, 1973.Riordan, J. Combinatorial
Identities. New York: Wiley, 1979.Weisstein, Eric W. "Gould and Hsu Matrix Inversion Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GouldandHsuMatrixInversionFormula.html