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A058962
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2^(2*n)*(2*n+1).
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14
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1, 12, 80, 448, 2304, 11264, 53248, 245760, 1114112, 4980736, 22020096, 96468992, 419430400, 1811939328, 7784628224, 33285996544, 141733920768, 601295421440, 2542620639232, 10720238370816, 45079976738816, 189115999977472, 791648371998720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Denominators in expansion of -1/2*I*Pi+I*arcsin((1+1/4*x^2)/(1-1/4*x^2)); numerators are all 1.
Bisection of A001787. That is, a(n)=A001787(2n+1) - Graeme McRae (g_m(AT)mcraefamily.com), Jul 12 2006
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REFERENCES
| G. A. Campbell, Physical theory of the electric wave-filter, Bell Syst. Tech. J., 1 (1922), 1-32, see Eq. (15d). Reprinted in M. E. Van Valkebburg, ed., Circuit Theory, Dowden, Hutchinson and Ross, 1974.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,200
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FORMULA
| Central terms of the triangle in A118413: a(n) = A118413(2*n+1,n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 27 2006
ln(3) = sum( 1 / a(n) ) for n = 0..infinity - Jaume Oliver i Lafont (jaume(AT)totmallorca.net), May 22 2007
a(n) = 4((2n+1)/(2n-1))a(n-1) = 4a(n-1)+2^(2n+1) = 8a(n-1)-16a(n-2) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 09 2008]
G.f.: (1+4*x)/(1-4*x)^2 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Jan 29 2009]
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MAPLE
| a:=n->sum (4^n*n^binomial(j, n)/4, j=1..n): seq(a(n), n=1..23); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]
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PROG
| (PARI) { for (n = 0, 200, write("b058962.txt", n, " ", 2^(2*n)*(2*n+1)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 24 2009]
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CROSSREFS
| Cf. A118415.
Cf. A002391.
Cf. A154920. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Jan 29 2009]
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Factor of the LS1[ -2,n] matrix coefficients in A160487.
(End)
Sequence in context: A190216 A160559 A038734 * A203486 A009500 A012195
Adjacent sequences: A058959 A058960 A058961 * A058963 A058964 A058965
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 13 2001
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EXTENSIONS
| Limit of summation corrected by Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Jan 26 2009
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