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 A052141 Number of paths from (0,0) to (n,n) that always move closer to (n,n) (and do not pass (n,n) and backtrack). 7
 1, 3, 26, 252, 2568, 26928, 287648, 3112896, 34013312, 374416128, 4145895936, 46127840256, 515268544512, 5775088103424, 64912164888576, 731420783788032, 8259345993203712, 93443504499523584, 1058972245409005568, 12019152955622817792, 136599995048232747008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 6.3.9. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA G.f.: 1/2 + 1/(2*(1 - 12*x + 4*x^2)^(1/2)). a(n) = A001850(n)*2^(n-1). - Jon Stadler (jstadler(AT)capital.edu), Apr 30 2003 Recurrence: n*a(n) = 6*(2*n-1)*a(n-1) - 4*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 08 2012 a(n) ~ sqrt(8+6*sqrt(2))*(6+4*sqrt(2))^n/(8*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 08 2012 MATHEMATICA a[0] = 1; a[n_] := Hypergeometric2F1[-n, n+1, 1, -1]*2^(n-1); Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Feb 23 2012, after Jon Stadler *) CROSSREFS Main diagonal of A059576. Column k=2 of A316674. Cf. A084773, A316673. Sequence in context: A037797 A071846 A067858 * A062793 A300398 A048861 Adjacent sequences:  A052138 A052139 A052140 * A052142 A052143 A052144 KEYWORD nonn,easy,nice,walk AUTHOR N. J. A. Sloane, Jan 23 2000 STATUS approved

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Last modified October 15 08:45 EDT 2018. Contains 316210 sequences. (Running on oeis4.)