On some identities for the Fibonomial coefficients

Jaroslav Seibert; Pavel Trojovský

Mathematica Slovaca (2005)

  • Volume: 55, Issue: 1, page 9-19
  • ISSN: 0232-0525

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Seibert, Jaroslav, and Trojovský, Pavel. "On some identities for the Fibonomial coefficients." Mathematica Slovaca 55.1 (2005): 9-19. <http://eudml.org/doc/32000>.

@article{Seibert2005,
author = {Seibert, Jaroslav, Trojovský, Pavel},
journal = {Mathematica Slovaca},
keywords = {Fibonacci number; Lucas number; Fibonomial coefficient; generating function},
language = {eng},
number = {1},
pages = {9-19},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On some identities for the Fibonomial coefficients},
url = {http://eudml.org/doc/32000},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Seibert, Jaroslav
AU - Trojovský, Pavel
TI - On some identities for the Fibonomial coefficients
JO - Mathematica Slovaca
PY - 2005
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 55
IS - 1
SP - 9
EP - 19
LA - eng
KW - Fibonacci number; Lucas number; Fibonomial coefficient; generating function
UR - http://eudml.org/doc/32000
ER -

References

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  1. CARLITZ L., Generating functions for powers of a certain sequence of numbers, Duke Math. J. 29 (1962), 521-537. (1962) MR0140476
  2. FONTENÉ G., Généralisation ďune formule connue, Nouv. Ann. (4) 15 (1915), 112. (1915) 
  3. GOULD H. W., The bracket function and Fontené Ward generalized binomial coefficients with application to Fibinomial coefficients, Fibonacci Quart. 7 (1969), 23-40. (1969) MR0242691
  4. HORADAM A. F., Generating functions for powers of a certain generalized sequence of numbers, Duke Math. J. 32 (1965), 437-446. (1965) Zbl0131.04104MR0177975
  5. HOLTE J. M., Residues of generalized binomial coefficients modulo primes, Fibonacci Quart. 38 (2000), 227-238. MR1756791
  6. JARDEN D., Recurring sequences, Riveon Lematimatika (Israel) (1958). (1958) MR0098201
  7. RIORDAN J., Generating functions for powers of Fibonacci numbers, Duke Math. J. 29 (1962), 5-12. (1962) Zbl0101.28801MR0132023
  8. SHANNON A. G., A method of Carlitz applied to the k-th power generating function for Fibonacci numbers, Fibonacci Quart. 12 (1974), 293-299. (1974) Zbl0287.10010MR0349570
  9. TORRETTO R.- FUCHS A., Generalized binomial coefficients, Fibonacci Quart. 2 (1964), 296-302. (1964) MR0173655
  10. [unknown], http:/www.search.att.com/projects/OEIS=A0055870. 

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