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%I #10 Jan 17 2019 03:10:34
%S 1,28,462,6832,97957,1394180,19862674,284156608,4086496362,
%T 59089988216,858975619676,12549322976672,184195104642157,
%U 2715174884250004,40181870424263146,596810833742837536,8893877150513222014,132947157383427373320,1992954280253792526660
%N Coefficients related to tennis ball problem.
%H G. C. Greubel, <a href="/A079518/b079518.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,3) = 1*t^4 + 28*t^6 + 462*t^8 + 6832*t^10 + ... - _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, 3], {t,0,60}], t][[1;; ;;2]], 2] (* _G. C. Greubel_, Jan 16 2019 *)
%Y Cf. A079513, A079514, A079515, A079516, A079517, 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
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