The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A176027 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A176027

Binomial transform of A005563.
(history; published version)

#38 by Michael De Vlieger at Sat Aug 13 06:22:39 EDT 2022

STATUS

reviewed

approved

#37 by Michel Marcus at Sat Aug 13 06:07:34 EDT 2022

STATUS

proposed

reviewed

#36 by Amiram Eldar at Sat Aug 13 04:07:24 EDT 2022

STATUS

editing

proposed

#35 by Amiram Eldar at Sat Aug 13 04:04:25 EDT 2022

FORMULA

a(n) = 2*a(n-1) + A001792(n).

a(n) = A001793(n) - 2^(n-1) for n > 0. - Brad Clardy, Mar 02 2012

From Amiram Eldar, Aug 13 2022: (Start)

Sum_{n>=1} 1/a(n) = 1322/75 - 124*log(2)/5.

Sum_{n>=1} (-1)^(n+1)/a(n) = 132*log(3/2)/5 - 782/75. (End)

PROG

(MAGMAMagma) [2^(n-2)*n*(5+n) : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011

CROSSREFS

Cf. A001792, A001793, A005563, A058396, A084266, A127276.

STATUS

approved

editing

#34 by Charles R Greathouse IV at Thu Sep 21 01:31:03 EDT 2017

STATUS

editing

approved

#33 by Charles R Greathouse IV at Thu Sep 21 01:30:54 EDT 2017

FORMULA

G.f.: x*(-3+4*x)/(2*x-1)^3. [_- _R. J. Mathar_, Dec 11 2010]

a(n) = 2^(n-2)*n*(5+n). [_- _R. J. Mathar_, Dec 11 2010]

a(n) = A127276(n) - A127276(n+1).

a(n) = A001793(n)-2^(n-1) for n > 0. [_- _Brad Clardy_, Mar 02 2012]

PROG

(PARI) a(n)=n*(n+5)<<(n-2) \\ Charles R Greathouse IV, Sep 21 2017

STATUS

proposed

editing

#32 by Michel Marcus at Thu Sep 21 01:27:38 EDT 2017

STATUS

editing

proposed

#31 by Michel Marcus at Thu Sep 21 01:27:33 EDT 2017

FORMULA

G.f.: x*(-3+4*x)/(2*x-1)^3. [_R. J. Mathar, _, Dec 11 2010]

a(n) = 2^(n-2)*n*(5+n). [_R. J. Mathar, _, Dec 11 2010]

a(n) = A001793(n)-2^(n-1) for n > 0. [_Brad Clardy, _, Mar 02 2012]

STATUS

proposed

editing

#30 by Wesley Ivan Hurt at Wed Sep 20 17:32:13 EDT 2017

STATUS

editing

proposed

#29 by Wesley Ivan Hurt at Wed Sep 20 17:21:02 EDT 2017

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).

FORMULA

a(n) = (1/32) * Sum_{k=0..n+4-1} Sum_{i=0..n+4-1} (k-2+3) * C(n+4,-1,i). - Wesley Ivan Hurt, Sep 20 2017