

A075045


Coefficients A_n for the s=3 tennis ball problem.


1



1, 9, 69, 502, 3564, 24960, 173325, 1196748, 8229849, 56427177, 386011116, 2635972920, 17974898872, 122430895956, 833108684637, 5664553564440, 38488954887171, 261369752763963, 1774016418598269, 12035694958994142, 81624256468292016, 553377268856455968
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..21.
R. Bacher, On generating series of complementary plane trees arXiv:math/0409050 [math.CO], 2004.
D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), pp. 307344 (A_n for s=3).


FORMULA

G.f.: seems to be (3*g1)^(2)*(1g)^(3) where g*(1g)^2 = x.  Mark van Hoeij, Nov 10 2011
a(n) = (6*(252*n^3 + 477*n^2 + 220*n + 11)*a(n1)  81*(63*n^3 + 72*n^2  7*n  8)*a(n2))/(8*(14*n^3 + 37*n^2 + 26*n + 3)) for n > 2.  conjectured by JeanFrançois Alcover, Feb 07 2019


CROSSREFS

See A049235 for more information.
Sequence in context: A198691 A125372 A165147 * A081616 A299915 A287818
Adjacent sequences: A075042 A075043 A075044 * A075046 A075047 A075048


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Jan 19 2003


STATUS

approved



