A079516 - OEIS

%I #12 Jan 17 2019 03:10:38

%S 1,15,185,2304,29482,386945,5188169,70803164,980545070,13747777966,

%T 194776025482,2784380900560,40113386761524,581823363803941,

%U 8489505340500521,124528817146723876,1835299404114540102,27163404479642455346,403573421012802035630

%N Coefficients related to tennis ball problem.

%H G. C. Greubel, <a href="/A079516/b079516.txt">Table of n, a(n) for n = 0..500</a>

%H D. Merlini, R. Sprugnoli and M. C. Verri, <a href="http://dx.doi.org/10.1006/jcta.2002.3273">The tennis ball problem</a>, J. Combin. Theory, A 99 (2002), 307-344. (Table A.3)

%F 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

%t 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 *)

%Y Cf. A079513, A079514, A079515, A079517, A079518, A079519.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 22 2003

%E Terms a(5) onward added by _G. C. Greubel_, Jan 16 2019