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 A079522 Diagonal of triangular array in A079520. 3
 0, 1, 3, 10, 31, 105, 343, 1198, 4056, 14506, 50350, 183284, 647809, 2390121, 8564543, 31933830, 115664164, 434920398, 1588917802, 6016012236, 22134533070, 84289034154, 311957090678, 1193717733900, 4440128821376, 17060985356980, 63732279047612, 245768668712296, 921501110779045 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344. (Fig A.3) FORMULA Let c, d, and g be given by: 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*c(t))^r*(t*c(t)^3 + 2*r*c(t)) then the g.f. is given by the expansion of g(t,0). - G. C. Greubel, Jan 17 2019 EXAMPLE G.f. = 0 + 1*t + 3*t^2 + 10*t^3 + 31*t^4 + ... - G. C. Greubel, Jan 17 2019 MAPLE F := proc(t) (1-4*t^2-(1+2*t)*sqrt(1-4*t)-(1-2*t)*sqrt(1+4*t)+ sqrt(1-16*t^2))/4/t^3 ; end: d := proc(t) 1+t*F(t) ; end: C := proc(t) (1-sqrt(1-4*t))/2/t ; end: A079521 := proc(h, r) d(t)*t^(r+1)*(C(t))^(r+3) ; expand(%) ; coeftayl(%, t=0, h) ; end: A079522 := proc(n) A079521(n, 0) ; end: for n from 0 do printf("%d\n", A079522(n)) ; od: # R. J. Mathar, Sep 20 2009 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*c[t])^r*(t*c[t]^3 +2*r*c[t]); CoefficientList[Series[g[t, 0], {t, 0, 50}], t] (* G. C. Greubel, Jan 17 2019 *) CROSSREFS Also diagonal of triangular array in A079521. Cf. A079513, A079520. Sequence in context: A005510 A005725 A302287 * A325579 A034016 A001403 Adjacent sequences:  A079519 A079520 A079521 * A079523 A079524 A079525 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 22 2003 EXTENSIONS More terms from R. J. Mathar, Sep 20 2009 Terms a(23) onward added by G. C. Greubel, Jan 17 2019 STATUS approved

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Last modified May 30 15:21 EDT 2020. Contains 334726 sequences. (Running on oeis4.)