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A052473 a(n) = binomial(2*n-5,n-2) + 2. 1
2, 2, 3, 3, 5, 12, 37, 128, 464, 1718, 6437, 24312, 92380, 352718, 1352080, 5200302, 20058302, 77558762, 300540197, 1166803112, 4537567652, 17672631902, 68923264412, 269128937222, 1052049481862, 4116715363802, 16123801841552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The best upper bound known for the Erdős-Szekeres problem for n >= 6.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Happy End Problem

FORMULA

a(n) = 2 + (2^(-5 + 2*n) gamma(-(3/2) + n))/(sqrt(pi) gamma(-1 + n)).

G.f.: (4 - ((1 + sqrt(1 - 4*x)) (-1 + x)*x^2)/sqrt(1 - 4*x))/(2 - 2 x). - Eric W. Weisstein, Jul 29 2011

MATHEMATICA

Table[Binomial[2 n - 5, n - 2] + 2, {n, 0, 20}]

PROG

(PARI) a(n)=binomial(2*n-5, n-2)+2 \\ Charles R Greathouse IV, Jul 29 2011

CROSSREFS

Sequence in context: A102330 A103598 A103403 * A165122 A240505 A051715

Adjacent sequences:  A052470 A052471 A052472 * A052474 A052475 A052476

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified November 14 09:49 EST 2018. Contains 317182 sequences. (Running on oeis4.)