A079516 Coefficients related to tennis ball problem.

1, 15, 185, 2304, 29482, 386945, 5188169, 70803164, 980545070, 13747777966, 194776025482, 2784380900560, 40113386761524, 581823363803941, 8489505340500521, 124528817146723876, 1835299404114540102, 27163404479642455346, 403573421012802035630

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, A079517, A079518, A079519.

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, 1], {t, 0, 60}], t][[1 ;; ;; 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 even terms in the expansion of g(t,1) = 1*t^2 + 15*t^4 + 185*t^6 + 2304*t^8 + ... - G. C. Greubel, Jan 16 2019

Extensions

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