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A002696
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Binomial coefficients C(2n,n-3).
(Formerly M4532 N1921)
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4
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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; refs; listen; history; internal format)
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OFFSET
| 3,2
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COMMENTS
| 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
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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).
Milan Janjic, Two Enumerative Functions
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FORMULA
| 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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MATHEMATICA
| CoefficientList[ Series[ 64/(((Sqrt[1 - 4 x] + 1)^6)*Sqrt[1 - 4 x]), {x, 0, 22}], x] (* Robert G. Wilson v, Aug 08 2011 *)
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PROG
| (MAGMA) [ Binomial(2*n, n-3): n in [3..150] ]; // Vincenzo Librandi, Apr 13 2011
(PARI) a(n)=binomial(n+n, n-3) \\ Charles R Greathouse IV, Aug 08 2011
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CROSSREFS
| Diagonal 7 of triangle A100257.
Sequence in context: A097555 A055222 A026015 * A016208 A026852 A110609
Adjacent sequences: A002693 A002694 A002695 * A002697 A002698 A002699
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2004
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