The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A188267 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A188267

Coefficient of x^n in the series 1/(1-x*F(1/2,1/2;1;16x)), where F(a1,a2;b;x) is the hypergeometric series.
(history; published version)

#28 by Vaclav Kotesovec at Thu Oct 03 10:58:48 EDT 2019

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#27 by Vaclav Kotesovec at Thu Oct 03 09:58:01 EDT 2019

CROSSREFS

Cf. A188266, A328046.

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editing

#26 by Vaclav Kotesovec at Tue Oct 01 09:32:45 EDT 2019

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#25 by Vaclav Kotesovec at Tue Oct 01 09:32:29 EDT 2019

LINKS

Vaclav Kotesovec, <a href="/A188267/a188267.jpg">Graph - the asymptotic ratio (10000 terms)</a>

#24 by Vaclav Kotesovec at Tue Oct 01 09:14:58 EDT 2019

FORMULA

a(n) ~ Pi * 2^(4*n + 4) / (n * (log(n) - 16*Pi)^2) * (1 - 2*(gamma + 4*log(2)) / (log(n) - 16*Pi) + (3*gamma^2 - Pi^2/2 + 24*gamma*log(2) + 48*log(2)^2) / (log(n) - 16*Pi)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 01 2019

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#23 by Vaclav Kotesovec at Mon Sep 30 09:09:03 EDT 2019

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#22 by Vaclav Kotesovec at Mon Sep 30 08:51:04 EDT 2019

FORMULA

G.f.: 1/(1 - x/AGM(sqrt(1 - 16*x), 1)). - Vaclav Kotesovec, Sep 30 2019

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#21 by Vaclav Kotesovec at Sat Sep 28 06:58:56 EDT 2019

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#20 by Vaclav Kotesovec at Sat Sep 28 06:58:46 EDT 2019

MATHEMATICA

a[0] = 1; Flatten[{1, Table[a[n+1] = Sum[Binomial[2*k, k]^2*a[n-k], {k, 0, n}], {n, 0, 20}]}] (* Vaclav Kotesovec, Sep 28 2019 *)

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#19 by Vaclav Kotesovec at Tue Apr 12 13:47:17 EDT 2016

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approved