The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A091485 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A091485

Number of labeled 2,3 cacti (triangular cacti with bridges).
(history; published version)

#27 by Michael De Vlieger at Sat Aug 19 19:04:07 EDT 2023

STATUS

proposed

approved

#26 by Seiichi Manyama at Sat Aug 19 09:09:17 EDT 2023

STATUS

editing

proposed

#25 by Seiichi Manyama at Sat Aug 19 09:07:12 EDT 2023

CROSSREFS

Cf. A091481, A091487, A000085.

#24 by Seiichi Manyama at Sat Aug 19 02:50:33 EDT 2023

FORMULA

a(n+1) = n! * Sum_{k=0..n} (1/2)^(n-k) * (n+1)^(k-1) * binomial(k,n-k)/k!. - Seiichi Manyama, Aug 19 2023

STATUS

approved

editing

#23 by Bruno Berselli at Mon Aug 06 10:56:58 EDT 2018

STATUS

proposed

approved

#22 by Jean-François Alcover at Mon Aug 06 10:48:51 EDT 2018

STATUS

editing

proposed

#21 by Jean-François Alcover at Mon Aug 06 10:48:48 EDT 2018

MATHEMATICA

CoefficientList[1/x InverseSeries[x/Exp[x+x^2/2]+O[x]^20], x] Range[0, 18]! (* Jean-François Alcover, Aug 06 2018 *)

STATUS

approved

editing

#20 by N. J. A. Sloane at Fri Jun 23 18:58:46 EDT 2017

STATUS

editing

approved

#19 by N. J. A. Sloane at Fri Jun 23 18:58:44 EDT 2017

COMMENTS

As Alois P. Heinz has pointed out, the e.g.f in the Example section does not match the offset. The However, the identity a(n) = A091481(n)/n holds with the present offset of 1. - N. J. A. Sloane, Jun 23 2017

STATUS

approved

editing

#18 by N. J. A. Sloane at Fri Jun 23 18:58:08 EDT 2017

STATUS

editing

approved