The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002544 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002544

a(n) = binomial(2*n+1,n)*(n+1)^2.
(history; published version)

#125 by N. J. A. Sloane at Tue Oct 18 19:10:58 EDT 2022

STATUS

editing

approved

#124 by N. J. A. Sloane at Tue Oct 18 19:10:55 EDT 2022

LINKS

J. Ser, <a href="/A002720/a002720_4.pdf">Les Calculs Formels des Séries de Factorielles</a>, Gauthier-Villars, Paris, 1933 [Local copy].

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approved

editing

#123 by Peter Luschny at Sat May 14 03:54:18 EDT 2022

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reviewed

approved

#122 by Vaclav Kotesovec at Sat May 14 03:43:30 EDT 2022

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proposed

reviewed

#121 by Amiram Eldar at Sat May 14 02:53:29 EDT 2022

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editing

proposed

#120 by Amiram Eldar at Sat May 14 02:35:03 EDT 2022

FORMULA

Sum_{n>=0} (-1)^n/a(n) = 4*arcsinh(1/2)^2 = A202543^2. - Amiram Eldar, May 14 2022

CROSSREFS

Cf. A085373, A002457, A002674, A202543.

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approved

editing

#119 by Michael De Vlieger at Tue May 03 10:59:35 EDT 2022

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proposed

approved

#118 by R. J. Mathar at Tue May 03 10:02:24 EDT 2022

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editing

proposed

#117 by R. J. Mathar at Tue May 03 10:02:04 EDT 2022

COMMENTS

Let cos(x) = 1 -x^2/2 +x^4/4!-x^6/6!.. = Sum_i (-1)^i x^(2i)/(2i)! be the standard power series of the cosine, and y = 2*(1-cos(x)) = 4*sin^2(x/2) = x^2 -x^4/12 +x^6/360 ...= Sum_i 2*(-1)^(i+1) x^(2i)/(2i)! be a closely related series. Then this sequence represents the reversion x^2 = Sum_i 1/a(i) *y^(i+1). - R. J. Mathar, May 03 2022

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approved

editing

#116 by Joerg Arndt at Wed Apr 27 10:01:41 EDT 2022

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reviewed

approved