The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115178 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A115178

Expansion of c(x^2+x^3), c(x) the g.f. of A000108.
(history; published version)

#26 by Alois P. Heinz at Tue Sep 10 20:47:34 EDT 2024

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proposed

approved

#25 by Jason Yuen at Tue Sep 10 20:46:01 EDT 2024

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editing

proposed

#24 by Jason Yuen at Tue Sep 10 20:45:52 EDT 2024

FORMULA

G.f. A(x) satisfies A(x) = 1 / (1 - x^2 / (1 - x / (1 - x^2 * A(x))))). - Michael Somos, May 12 2012

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approved

editing

#23 by R. J. Mathar at Wed Sep 29 09:35:43 EDT 2021

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editing

approved

#22 by R. J. Mathar at Wed Sep 29 09:35:39 EDT 2021

FORMULA

Conjecture: D-finite with recurrence (n+2)*a(n) +(n+2)*a(n-1) +4*(1-n)*a(n-2) +2*(7-4*n)*a(n-3) +2*(5-2*n)*a(n-4)=0. - R. J. Mathar, Nov 15 2011

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approved

editing

#21 by Alois P. Heinz at Fri Feb 03 14:57:38 EST 2017

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proposed

approved

#20 by G. C. Greubel at Fri Feb 03 14:07:56 EST 2017

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editing

proposed

#19 by G. C. Greubel at Fri Feb 03 14:07:45 EST 2017

LINKS

G. C. Greubel, <a href="/A115178/b115178.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(n) = sumSum_{k=0..floor(n/2), } C(k)*C(k,n-2k)}.

MATHEMATICA

Table[Sum[Binomial[k, n - 2*k]*CatalanNumber[k], {k, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, Feb 03 2017 *)

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approved

editing

#18 by Bruno Berselli at Mon Sep 16 18:33:20 EDT 2013

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proposed

approved

#17 by Vaclav Kotesovec at Mon Sep 16 16:16:52 EDT 2013

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editing

proposed