The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A181474 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A181474

Sequence related to the Hankel transform of A105523(n+5).
(history; published version)

#16 by OEIS Server at Tue Jul 25 10:58:49 EDT 2023

LINKS

Michael De Vlieger, <a href="/A181474/b181474_1.txt">Table of n, a(n) for n = 0..10000</a>

#15 by Michael De Vlieger at Tue Jul 25 10:58:49 EDT 2023

STATUS

proposed

approved

Discussion

Tue Jul 25

10:58

OEIS Server: Installed first b-file as b181474.txt.

#14 by Michel Marcus at Tue Jul 25 10:53:04 EDT 2023

STATUS

editing

proposed

#13 by Michel Marcus at Tue Jul 25 10:52:57 EDT 2023

LINKS

<a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).

FORMULA

a(n) = 2^n*(n+2)*(n+3)*Gamma(floor(n/2)+3)*Gamma(floor((n+1)/2)+1/2)/(12n!*sqrt(piPi)) (suggested by WolframAlpha).

a(n) = +a(n-1) +4*a(n-2) -4*a(n-3) -6*a(n-4) +6*a(n-5) +4*a(n-6) -4*a(n-7) -a(n-8) +a(n-9). a(n) = (n+3)*(n+2)*(2*n^2+2*(-1)^n*n+10*n+5*(-1)^n+11)/96. [From __R. J. Mathar_, Oct 23 2010]

STATUS

proposed

editing

#12 by Michael De Vlieger at Tue Jul 25 10:50:38 EDT 2023

STATUS

editing

proposed

#11 by Michael De Vlieger at Tue Jul 25 10:50:35 EDT 2023

LINKS

Michael De Vlieger, <a href="/A181474/b181474_1.txt">Table of n, a(n) for n = 0..10000</a>

MATHEMATICA

CoefficientList[Series[(1 + x + 4 x^2 + x^3 + x^4)/((1 - x)^5 (1 + x)^4), {x, 0, 36}], x] (* Michael De Vlieger, Jul 25 2023 *)

#10 by Michael De Vlieger at Tue Jul 25 10:44:18 EDT 2023

LINKS

Nathaniel K. Green and Edward D. Kim, <a href="https://arxiv.org/abs/2307.06311">Further techniques on a polynomial positivity question of Collins, Dykema, and Torres-Ayala</a>, arXiv:2307.06311 [math.OC], 2023. See p. 18.

STATUS

approved

editing

#9 by Charles R Greathouse IV at Sat Jun 13 00:53:40 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).

Discussion

Sat Jun 13

00:53

OEIS Server: https://oeis.org/edit/global/2439

#8 by Charles R Greathouse IV at Fri Jun 12 15:27:32 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,4,-4,-6,6,4,-4,-1,1).

Discussion

Fri Jun 12

15:27

OEIS Server: https://oeis.org/edit/global/2436

#7 by Charles R Greathouse IV at Fri Sep 14 03:39:31 EDT 2012

STATUS

editing

approved