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Search: id:A001448
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| A001448 |
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C(4n,2n) = (4*n)!/((2*n)!*(2*n)!). |
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+0
7
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| 1, 6, 70, 924, 12870, 184756, 2704156, 40116600, 601080390, 9075135300, 137846528820, 2104098963720, 32247603683100, 495918532948104, 7648690600760440, 118264581564861424, 1832624140942590534
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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Using Stirling's formula in sequence A000142 it is easy to get the asymptotic expression a(n) ~ 16^n / sqrt(2 * Pi * n) - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001
a(n)= 2*A001700(2*n-1) = (2*n+1)*C(2*n), n >= 1, C(n) := A000108(n) (Catalan). G.f.: (1-y*((1+4*y)*c(y)-(1-4*y)*c(-y)))/(1-(4*y)^2) with y^2=x, c(y)= g.f. for A000108 (Catalan). - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Dec 13 2001
a(n) ~ 2^(-1/2)*pi^(-1/2)*n^(-1/2)*2^(4*n)*{1 - 1/16*n^-1 + ...} - Joe Keane (jgk(AT)jgk.org), Jun 11 2002
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MAPLE
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f := n->(4*n)!/((2*n)!*(2*n)!);
a:=n->sum(binomial(2*n, n)/(n+1), j=0..n): seq(a(n*2), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007
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CROSSREFS
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Bisection of A000984. Cf. A002458.
Sequence in context: A098639 A048708 A104900 this_sequence A024489 A036361 A050788
Adjacent sequences: A001445 A001446 A001447 this_sequence A001449 A001450 A001451
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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