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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 (list; graph; refs; listen; history; text; internal format)
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. 307-344 (A_n for s=3).

FORMULA

G.f.: seems to be (3*g-1)^(-2)*(1-g)^(-3) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011

a(n) = (6*(252*n^3 + 477*n^2 + 220*n + 11)*a(n-1) - 81*(63*n^3 + 72*n^2 - 7*n - 8)*a(n-2))/(8*(14*n^3 + 37*n^2 + 26*n + 3)) for n > 2. - conjectured by Jean-Fran├žois 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

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Last modified December 5 12:04 EST 2020. Contains 338947 sequences. (Running on oeis4.)