The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A206849 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A206849

a(n) = Sum_{k=0..n} binomial(n^2, k^2).
(history; published version)

#23 by Alois P. Heinz at Sat Jan 19 06:42:36 EST 2019

STATUS

reviewed

approved

#22 by Michel Marcus at Sat Jan 19 06:16:21 EST 2019

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proposed

reviewed

#21 by Seiichi Manyama at Sat Jan 19 06:02:05 EST 2019

STATUS

editing

proposed

#20 by Seiichi Manyama at Sat Jan 19 06:01:27 EST 2019

LINKS

Seiichi Manyama, <a href="/A206849/b206849.txt">Table of n, a(n) for n = 0..57</a>

STATUS

approved

editing

#19 by Vaclav Kotesovec at Mon Mar 03 06:08:28 EST 2014

STATUS

editing

approved

#18 by Vaclav Kotesovec at Mon Mar 03 06:07:48 EST 2014

LINKS

Vaclav Kotesovec, <a href="/A206849/a206849.jpg">Limits, graph for 500 terms</a>

#17 by Vaclav Kotesovec at Mon Mar 03 05:47:21 EST 2014

FORMULA

From Vaclav Kotesovec, Mar 03 2014: (Start)

Limit n->infinity a(n)^(1/n^2) = 2

Lim sup n->infinity a(n)/(2^(n^2)/n) = sqrt(2/Pi) * JacobiTheta3(0,exp(-4)) = Sqrt[2/Pi] * EllipticTheta[3, 0, 1/E^4] = 0.827112271364145742...

Lim inf n->infinity a(n)/(2^(n^2)/n) = sqrt(2/Pi) * JacobiTheta2(0,exp(-4)) = Sqrt[2/Pi] * EllipticTheta[2, 0, 1/E^4] = 0.587247586271786487...

(End)

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approved

editing

#16 by Bruno Berselli at Mon Mar 03 03:51:47 EST 2014

STATUS

editing

approved

#15 by Vaclav Kotesovec at Mon Mar 03 03:37:55 EST 2014

FORMULA

Ignoring the initial term a(0), equals the logarithmic derivative of A206848.

MATHEMATICA

Table[Sum[Binomial[n^2, k^2], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 03 2014 *)

STATUS

approved

editing

#14 by Paul D. Hanna at Sat Sep 21 01:09:34 EDT 2013

STATUS

editing

approved