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A052227
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(4*n+1)*binomial(3*n,n)/(2*n+1).
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2
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1, 5, 27, 156, 935, 5733, 35700, 224808, 1427679, 9126975, 58659315, 378658800, 2453288292, 15944020316, 103897691640, 678610095504, 4441369072335, 29120107628115, 191233066114545, 1257635016353100
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| T(2n,n) for A111125. - Paul Barry (pbarry(AT)wit.ie), Apr 19 2007
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
| G.f.: 4*x*F(4/3,5/3;5/2;27*x/4) + 2*sin(1/3*arcsin((3*sqrt(3*x))/2))/sqrt(3*x), where F(a;b;z) is a hypergeometric series. [Emanuele Munarini, Jun 06 2011]
G.f.: (g+1)/((3*g-1)*(g-1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011
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MATHEMATICA
| Table[(4n + 1)Binomial[3n, n]/(2n + 1), {n, 0, 30}] (* From Harvey P. Dale, Jan 31 2011 *)
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PROG
| (Maxima) makelist(binomial(3*n, n)*(4*n+1)/(2*n+1), n, 0, 100); [Emanuele Munarini, Jun 6 2011]
(MAGMA) [(4*n+1)*Binomial(3*n, n)/(2*n+1) : n in [0..30]]; // Vincenzo Librandi, Nov 13 2011
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CROSSREFS
| Cf. A045721.
Sequence in context: A083326 A083880 A098409 * A101386 A153233 A084076
Adjacent sequences: A052224 A052225 A052226 * A052228 A052229 A052230
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jan 29 2000
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EXTENSIONS
| More terms from Harvey P. Dale, Jan 31 2011
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