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A049235
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Sum of balls on the lawn for the s=3 tennis ball problem.
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7
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0, 6, 75, 708, 5991, 47868, 369315, 2783448, 20631126, 151026498, 1094965524, 7878119760, 56330252412, 400703095284, 2838060684483, 20027058300144, 140874026880204, 988194254587242, 6915098239841331, 48285969880645908, 336521149274459979
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| D. Merlini, R. Sprugnoli and M. C. Verri, The tennis ball problem, J. Combin. Theory, A 99 (2002), 307-344 (S_n for s=3).
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FORMULA
| a(n) is asymptotic to c*sqrt(n)*(27/4)^n with c=2.4... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003
G.f.: F(G^(-1)(x)) where F = 3*(2-3*t)*t*((t-1)*(3*t-1))^(-3) and G = t*(t-1)^2 - Mark van Hoeij, Oct 30 2011.
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MAPLE
| T := (n, s)->binomial(s*n, n)/((s-1)*n+1); Y := (n, s)->add(binomial(s*k, k)*binomial(s*(n-k), n-k), k=0..n); A := (n, s)->Y(n+1, s)/2-(1/2)*((2*s-3)*n+2*s-2)*T(n+1, s); S := (n, s)->(1/2)*(s*n^2+(3*s-1)*n+2*s)*T(n+1, s)-Y(n+1, s)/2;
F := 3*(2-3*t)*t*((t-1)*(3*t-1))^(-3); G := t*(t-1)^2; Ginv := RootOf(G-x, t);
ogf := series(eval(F, t=Ginv), x=0, 20);
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CROSSREFS
| The four sequences T_n, Y_n, A_n, S_n for s=2 are A000108, A000302, A000346, A031970, for s=3, A001764, A006256, A075045, this sequence, for s=4, A002293, A078995, A078999, A078516.
Cf. A079486.
Sequence in context: A057783 A177561 A069852 * A129031 A139088 A193784
Adjacent sequences: A049232 A049233 A049234 * A049236 A049237 A049238
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2003
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