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 A079518 Coefficients related to tennis ball problem. 6
 1, 28, 462, 6832, 97957, 1394180, 19862674, 284156608, 4086496362, 59089988216, 858975619676, 12549322976672, 184195104642157, 2715174884250004, 40181870424263146, 596810833742837536, 8893877150513222014, 132947157383427373320, 1992954280253792526660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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) 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,3) = 1*t^4 + 28*t^6 + 462*t^8 + 6832*t^10 + ... - G. C. Greubel, Jan 16 2019 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, 3], {t, 0, 60}], t][[1;; ;; 2]], 2] (* G. C. Greubel, Jan 16 2019 *) CROSSREFS Cf. A079513, A079514, A079515, A079516, A079517, A079519. Sequence in context: A000771 A327508 A215767 * A320820 A160060 A115226 Adjacent sequences: A079515 A079516 A079517 * A079519 A079520 A079521 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 22 2003 EXTENSIONS Terms a(5) onward added by G. C. Greubel, Jan 16 2019 STATUS approved

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Last modified May 25 17:30 EDT 2024. Contains 372804 sequences. (Running on oeis4.)