A079515 Coefficients related to tennis ball problem.

1, 10, 105, 1198, 14506, 183284, 2390121, 31933830, 434920398, 6016012236, 84289034154, 1193717733900, 17060985356980, 245768668712296, 3564709196133737, 52015567131639798, 763050542202081318, 11246882679872658140, 166478073780305341390, 2473696423451621878180

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