A079517 Coefficients related to tennis ball problem.

1, 21, 301, 4088, 55354, 756059, 10442117, 145803900, 2056351566, 29262470042, 419730456306, 6062949606496, 88127311401876, 1288120149337735, 18922077118169717, 279209456350438708, 4136682188907493702, 61513664658938124486, 917795824360157700870

Offset: 0

Author

N. J. A. Sloane, Jan 22 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344. (Table A.3)

Crossrefs

Cf. A079513, A079514, A079515, A079516, A079518.

Programs

Mathematica

c[t_]:= (1-Sqrt[1-4*t])/(2*t); d[t_]:= (1-(1+2*t)*Sqrt[1-4*t] -(1-2*t)*Sqrt[1+4*t] +Sqrt[1-16*t^2])/(4*t^2); g[t_, r_]:= d[t]*t^(r+1)*c[t]^(r+3); Drop[CoefficientList[Series[g[t, 2], {t, 0, 60}], t][[2 ;; ;; 2]], 1] (* G. C. Greubel, Jan 16 2019 *)

Formula

With c(t) = (1 - sqrt(1-4*t))/(2*t), d(t) = (1 -(1+2*t)*sqrt(1-4*t) -(1 - 2*t)*sqrt(1+4*t) + sqrt(1-16*t^2))/(4*t^2), and g(t, r) = d(t)*t^(r + 1)*c(t)^(r + 3) then the g.f. is given by the odd terms in the expansion of g(t,2) = 1*t^3 + 21*t^5 + 301*t^7 + 4088*t^9 + ... - G. C. Greubel, Jan 16 2019

Extensions

Terms a(5) onward added by G. C. Greubel, Jan 16 2019