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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). 4
1, 3, 26, 252, 2568, 26928, 287648, 3112896, 34013312, 374416128, 4145895936, 46127840256, 515268544512, 5775088103424, 64912164888576, 731420783788032, 8259345993203712, 93443504499523584, 1058972245409005568, 12019152955622817792 (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-Fran├žois Alcover, Feb 23 2012, after Jon Stadler *)

CROSSREFS

Main diagonal of A059576.

Cf. A084773.

Sequence in context: A037797 A071846 A067858 * A062793 A048861 A053972

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 February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)