The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A105597

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A105597

Central numbers in a Moebius-binomial triangle.
(history; published version)

#11 by Peter Luschny at Wed Jan 24 01:21:12 EST 2024

STATUS

reviewed

approved

#10 by Michel Marcus at Wed Jan 24 00:49:33 EST 2024

STATUS

proposed

reviewed

#9 by James C. McMahon at Tue Jan 23 17:29:50 EST 2024

STATUS

editing

proposed

#8 by James C. McMahon at Tue Jan 23 17:28:29 EST 2024

MATHEMATICA

a[n_]:= Binomial[Abs[MoebiusMu[n]], Abs[MoebiusMu[Floor[n/2]]]]; Table[a[n], {n, 0, 100}] (* James C. McMahon, Jan 23 2024 *)

STATUS

approved

editing

#7 by N. J. A. Sloane at Sun Aug 27 23:23:29 EDT 2017

STATUS

proposed

approved

#6 by Antti Karttunen at Sun Aug 27 11:06:57 EDT 2017

STATUS

editing

proposed

#5 by Antti Karttunen at Sun Aug 27 11:02:43 EDT 2017

COMMENTS

Central numbers in A105595. Partial sums are A105598.

There seems to be a typo in above comment, maybe A105594 was intended? - Antti Karttunen, Aug 27 2017

Partial sums are A105598.

LINKS

Antti Karttunen, <a href="/A105597/b105597.txt">Table of n, a(n) for n = 0..65537</a>

Discussion

Sun Aug 27

11:03

Antti Karttunen: Partial sums of the b-file I computed match with the 10000 term b-file of A105598 computed by Vincenzo Librandi. I'll ask Paul Barry about this.

11:06

Antti Karttunen: ... because central terms of https://oeis.org/A105594 do NOT seem to match with this. But maybe Barry means with "central terms" something different than what I think.

#4 by Antti Karttunen at Sun Aug 27 10:31:34 EDT 2017

LINKS

<a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

FORMULA

a(n) = binomial(abs(mu(n)), abs(mu(floor(n/2)))).

PROG

(PARI) A105597(n) = if(n<2, 1, binomial(abs(moebius(n)), abs(moebius(n\2)))); \\ Antti Karttunen, Aug 27 2017

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:59:06 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Apr 14 2005

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

a(n)=binomial(abs(mu(n)), abs(mu(floor(n/2)))).

KEYWORD

easy,nonn,new