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
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