The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A075045 Coefficients A_n for the s=3 tennis ball problem. 2
 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. T. Amdeberhan, Integrality of a sum. R. Bacher, On generating series of complementary plane trees, arXiv:math/0409050 [math.CO], 2004. Toufik Mansour, I. L. Ramirez, Enumerations of polyominoes determined by Fuss-Catalan words, Australas. J. Combin. 81 (3) (2021) 447-457, table 1. 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 Conjecture: D-finite with recurrence 8*(2*n+3)*(7*n+1)*(n+1)*a(n) +6*(-252*n^3-477*n^2-220*n-11)*a(n-1) +81*(7*n+8)*(3*n-1)*(3*n+1)*a(n-2)=0. - Jean-François Alcover, Feb 07 2019 a(n) = (3n+2)*(n+1)*binomial(3n+3,n+1)/2/(2n+3) -A049235(n). [Merlini Theorem 2.5 for s=3] - R. J. Mathar, Oct 01 2021 MAPLE FussArea := proc(s, n) local a, i, j ; a := binomial((s+1)*n, n)*n/(s*n+1) ; ; add(j *(n-j) *binomial((s+1)*j, j) *binomial((s+1)*(n-j), n-j) /(s*j+1) /(s*(n-j)+1), j=0..n) ; a := a+binomial(s+1, 2)*% ; for j from 0 to n-1 do for i from 0 to j do i*(j-i) /(s*i+1) /(s*(j-i)+1) /(n-j) *binomial((s+1)*i, i) *binomial((s+1)*(j-i), j-i) *binomial((s+1)*(n-j)-2, n-1-j) ; a := a-%*binomial(s+1, 2) ; end do: end do: a ; end proc: seq(FussArea(2, n), n=1..30) ; # R. J. Mathar, Mar 31 2023 MATHEMATICA FussArea[s_, n_] := Module[{a, i, j, pc}, a = Binomial[(s + 1)*n, n]*n/(s*n + 1); pc = Sum[j*(n - j)*Binomial[(s + 1)*j, j]*Binomial[(s + 1)*(n - j), n - j]/(s*j + 1)/(s*(n - j) + 1), {j, 0, n}]; a = a + Binomial[s + 1, 2]*pc; For[j = 0, j <= n - 1 , j++, For[i = 0, i <= j, i++, pc = i*(j - i)/(s*i + 1)/(s*(j - i) + 1)/(n - j)*Binomial[(s + 1)*i, i]* Binomial[(s + 1)*(j - i), j - i]*Binomial[(s + 1)*(n - j) - 2, n - 1 - j]; a = a - pc*Binomial[s + 1, 2]; ]]; a]; Table[FussArea[2, n], {n, 1, 30}] (* Jean-François Alcover, Apr 02 2023, after R. J. Mathar *) CROSSREFS See A049235 for more information. Sequence in context: A198691 A125372 A165147 * A361139 A081616 A299915 Adjacent sequences: A075042 A075043 A075044 * A075046 A075047 A075048 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 19 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 1 13:52 EDT 2023. Contains 365826 sequences. (Running on oeis4.)