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A003516
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Binomial coefficients C(2n+1,n-2).
(Formerly M4417)
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8
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1, 7, 36, 165, 715, 3003, 12376, 50388, 203490, 817190, 3268760, 13037895, 51895935, 206253075, 818809200, 3247943160, 12875774670, 51021117810, 202112640600, 800472431850, 3169870830126, 12551759587422
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| a(n) = number of royal paths (A006318) from (0,0) to (n,n) with exactly one diagonal step off the line y=x. - David Callan (callan(AT)stat.wisc.edu), Mar 25 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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].
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FORMULA
| G.f.: 32*x^2/(((sqrt(1-4*x)+1)^5)*(sqrt(1-4*x))). [From Marco A. Cisneros Guevara, July 18 2011]
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MATHEMATICA
| CoefficientList[ Series[ 32/(((Sqrt[1 - 4 x] + 1)^5)*Sqrt[1 - 4 x]), {x, 0, 21}], x] (* Robert G. Wilson v, Aug 08 2011 *)
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PROG
| (MAGMA) [ Binomial(2*n+1, n-2): n in [2..150] ]; // Vincenzo Librandi, Apr 13 2011
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CROSSREFS
| Diagonal 6 of triangle A100257.
Sequence in context: A026018 A085354 A051198 * A095931 A026856 A038748
Adjacent sequences: A003513 A003514 A003515 * A003517 A003518 A003519
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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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