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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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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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, 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.
Sequence in context: A097555 A055222 A026015 this_sequence A016208 A026852 A110609
Adjacent sequences: A002693 A002694 A002695 this_sequence A002697 A002698 A002699
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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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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