# The Catalan Numbers. Part II 1

Formalized Mathematics (2006)

- Volume: 14, Issue: 4, page 153-159
- ISSN: 1426-2630

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topKarol Pąk. " The Catalan Numbers. Part II 1 ." Formalized Mathematics 14.4 (2006): 153-159. <http://eudml.org/doc/266549>.

@article{KarolPąk2006,

abstract = {In this paper, we define sequence dominated by 0, in which every initial fragment contains more zeroes than ones. If n ≥ 2 · m and n > 0, then the number of sequences dominated by 0 the length n including m of ones, is given by the formula [...] and satisfies the recurrence relation [...] Obviously, if n = 2 · m, then we obtain the recurrence relation for the Catalan numbers (starting from 0) [...] Using the above recurrence relation we can see that [...] where [...] and hence [...] MML identifier: CATALAN2, version: 7.8.03 4.75.958},

author = {Karol Pąk},

journal = {Formalized Mathematics},

language = {eng},

number = {4},

pages = {153-159},

title = { The Catalan Numbers. Part II 1 },

url = {http://eudml.org/doc/266549},

volume = {14},

year = {2006},

}

TY - JOUR

AU - Karol Pąk

TI - The Catalan Numbers. Part II 1

JO - Formalized Mathematics

PY - 2006

VL - 14

IS - 4

SP - 153

EP - 159

AB - In this paper, we define sequence dominated by 0, in which every initial fragment contains more zeroes than ones. If n ≥ 2 · m and n > 0, then the number of sequences dominated by 0 the length n including m of ones, is given by the formula [...] and satisfies the recurrence relation [...] Obviously, if n = 2 · m, then we obtain the recurrence relation for the Catalan numbers (starting from 0) [...] Using the above recurrence relation we can see that [...] where [...] and hence [...] MML identifier: CATALAN2, version: 7.8.03 4.75.958

LA - eng

UR - http://eudml.org/doc/266549

ER -

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