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%I #14 Jan 17 2019 03:10:25
%S 1,10,105,1198,14506,183284,2390121,31933830,434920398,6016012236,
%T 84289034154,1193717733900,17060985356980,245768668712296,
%U 3564709196133737,52015567131639798,763050542202081318,11246882679872658140,166478073780305341390,2473696423451621878180
%N Coefficients related to tennis ball problem.
%H G. C. Greubel, <a href="/A079515/b079515.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) [Column 1 of this table appears to be incorrect.]
%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 odd terms in the expansion of g(t,0) = t + 10*t^3 + 105*t^5 + 1198*t^7 + ... - _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); CoefficientList[Series[g[t, 0], {t, 0, 60}], t][[2 ;; ;; 2]] (* _G. C. Greubel_, Jan 16 2019 *)
%Y Cf. A079513, A079514, A079516, 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
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