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Search: id:A002696
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| A002696 |
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Binomial coefficients C(2n,n-3).
(Formerly M4532 N1921)
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+0
5
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| 1, 8, 45, 220, 1001, 4368, 18564, 77520, 319770, 1307504, 5311735, 21474180, 86493225, 347373600, 1391975640, 5567902560, 22239974430, 88732378800, 353697121050, 1408831480056, 5608233007146, 22314239266528, 88749815264600
(list; graph; listen)
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OFFSET
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3,2
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COMMENT
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Number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) which touch or cross the line x-y=3. - Herbert Kociemba (kociemba(AT)t-online.de), May 23 2004
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 517.
Robert Parviainen, Lattice Path Enumeration of Permutations with k Occurrences of the Pattern 2-13, Journal of Integer Sequences, Vol. 9 (2006), Article 06.3.2.
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LINKS
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Milan Janjic, Two Enumerative Functions
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].
A. Claesson and T. Mansour, Counting patterns of type (1,2) or (2,1).
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FORMULA
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G.f.: [1-sqrt(1-4z)]^6/[64z^3*sqrt(1-4z)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 28 2004
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CROSSREFS
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Diagonal 7 of triangle A100257.
Adjacent sequences: A002693 A002694 A002695 this_sequence A002697 A002698 A002699
Sequence in context: A097555 A055222 A026015 this_sequence A016208 A026852 A110609
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2004
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