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A079515 Coefficients related to tennis ball problem. 6
1, 10, 105, 1198, 14506, 183284, 2390121, 31933830, 434920398, 6016012236, 84289034154, 1193717733900, 17060985356980, 245768668712296, 3564709196133737, 52015567131639798, 763050542202081318, 11246882679872658140, 166478073780305341390, 2473696423451621878180 (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) [Column 1 of this table appears to be incorrect.]

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 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

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); CoefficientList[Series[g[t, 0], {t, 0, 60}], t][[2 ;; ;; 2]] (* G. C. Greubel, Jan 16 2019 *)

CROSSREFS

Cf. A079513, A079514, A079516, A079517, A079518, A079519.

Sequence in context: A046715 A145713 A123512 * A024131 A000457 A240681

Adjacent sequences:  A079512 A079513 A079514 * A079516 A079517 A079518

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 July 11 01:51 EDT 2020. Contains 335600 sequences. (Running on oeis4.)