A079517 Coefficients related to tennis ball problem.

1, 21, 301, 4088, 55354, 756059, 10442117, 145803900, 2056351566, 29262470042, 419730456306, 6062949606496, 88127311401876, 1288120149337735, 18922077118169717, 279209456350438708, 4136682188907493702, 61513664658938124486, 917795824360157700870

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 odd terms in the expansion of g(t,2) = 1*t^3 + 21*t^5 + 301*t^7 + 4088*t^9 + ... - 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, 2], {t, 0, 60}], t][[2 ;; ;; 2]], 1] (* G. C. Greubel, Jan 16 2019 *)

Crossrefs

Cf. A079513, A079514, A079515, A079516, A079518.

Sequence in context: A019664 A019839 A077513 * A021784 A019618 A081553

Adjacent sequences: A079514 A079515 A079516 * A079518 A079519 A079520

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