A079516 Coefficients related to tennis ball problem.

1, 15, 185, 2304, 29482, 386945, 5188169, 70803164, 980545070, 13747777966, 194776025482, 2784380900560, 40113386761524, 581823363803941, 8489505340500521, 124528817146723876, 1835299404114540102, 27163404479642455346, 403573421012802035630

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,1) = 1*t^2 + 15*t^4 + 185*t^6 + 2304*t^8 + ... - 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, 1], {t, 0, 60}], t][[1 ;; ;; 2]], 1] (* G. C. Greubel, Jan 16 2019 *)

Crossrefs

Cf. A079513, A079514, A079515, A079517, A079518, A079519.

Sequence in context: A193709 A157689 A273654 * A206521 A366662 A240796

Adjacent sequences: A079513 A079514 A079515 * A079517 A079518 A079519

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