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A007004
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(3*n)! / ((n+1)*(n!)^3).
(Formerly M3125)
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1
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1, 3, 30, 420, 6930, 126126, 2450448, 49884120, 1051723530, 22787343150, 504636071940, 11377249621920, 260363981732400, 6034149862347600, 141371511060715200, 3343436236585914480, 79726203788589122490
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of walks with steps (0,1)/North, (1,0)/East and (-1,-1)/Southwest from (0,0) to (0,0) of length 3n, and staying above the line y=x (i.e., any point (x,y) along the walk satisfies y>=x ). [From Shanzhen Gao (shanzhengao(AT)gmail.com), Nov 09 2010]
Number of walks in 3-dimensions using steps (1,0,0), (0,1,0), and (0,0,1) from (0,0,0) to (n,n,n) such that after each step we have y<=x. [From Eric Werley (erw309(AT)lehigh.edu), Jun 24 2011]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..150
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FORMULA
| a(n) = Binomial(2*n,n)*binomial(3*n,n)/(n+1) = A000108(n)*binomial(3*n,n) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 27 2006
a(n) = A060693(2n,n) = A088617(2n,n). - From DELEHAM Philippe, Nov 23 2011
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EXAMPLE
| n=1, three walks: NE(SW), (SW)NE, N(SW)E [From Shanzhen Gao (shanzhengao(AT)gmail.com), Nov 09 2010]
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MAPLE
| [seq(binomial(2*n, n)*binomial(3*n, n)/(n+1), n=0..17)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 27 2006
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MATHEMATICA
| a[n_]:=(3*n)!/((n + 1)*(n!)^3); [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 13 2008]
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PROG
| (MAGMA) [Factorial(3*n) / ((n+1)*Factorial(n)^3): n in [0..30]]; // Vincenzo Librandi, May 26 2011
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CROSSREFS
| Cf. A000108.
Sequence in context: A144283 A178016 A058831 * A012003 A164945 A201466
Adjacent sequences: A007001 A007002 A007003 * A007005 A007006 A007007
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jim Propp (propp(AT)math.wisc.edu)
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EXTENSIONS
| More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 27 2006
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