The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A099694 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A099694

Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled loops and arcs.
(history; published version)

#12 by N. J. A. Sloane at Tue Jan 12 21:30:51 EST 2021

STATUS

proposed

approved

#11 by Andrew Howroyd at Tue Jan 12 21:15:52 EST 2021

STATUS

editing

proposed

#10 by Andrew Howroyd at Tue Jan 12 20:20:39 EST 2021

NAME

Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

DATA

1, 2, 17, 244, 5283, 156092, 5954547, 282221828, 16159327961, 1094056231572, 86116276633357, 7773114989571400, 795480206815177651, 91417037615848058160, 11701283925663217478843, 1656436690705751478232180, 257730676653629520748175377, 43837005194184348815823808500

LINKS

Andrew Howroyd, <a href="/A099694/b099694.txt">Table of n, a(n) for n = 0..100</a>

FORMULA

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021

PROG

(PARI) \\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdlSeq defined in A098622.

R(n)={2*exp(x + O(x*x^n)) - x - 1}

EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

CROSSREFS

Cf. A014507, A098622, A099692, A099693, A099695.

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021

STATUS

approved

editing

#9 by N. J. A. Sloane at Sun Jun 25 15:13:14 EDT 2017

STATUS

editing

approved

#8 by N. J. A. Sloane at Sun Jun 25 15:13:12 EDT 2017

LINKS

G. Paquin, <a href="/A038205/a038205.pdf">Dénombrement de multigraphes enrichis</a>, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

STATUS

approved

editing

#7 by Jon E. Schoenfield at Fri Oct 23 06:52:20 EDT 2015

STATUS

editing

approved

#6 by Jon E. Schoenfield at Fri Oct 23 06:52:17 EDT 2015

REFERENCES

G. Paquin, D\'enombrement Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

STATUS

approved

editing

#5 by N. J. A. Sloane at Mon Oct 12 16:56:32 EDT 2015

REFERENCES

G. Paquin, D\'enombrement de multigraphes enrichis, M\'emoire, Mémoire, Math. Dept., Univ. Qu\'ebec \`a Montr\'eal, Québec à Montréal, 2004.

Discussion

Mon Oct 12

16:56

OEIS Server: https://oeis.org/edit/global/2464

#4 by Russ Cox at Fri Mar 30 16:50:04 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com), _, Oct 26 2004

Discussion

Fri Mar 30

16:50

OEIS Server: https://oeis.org/edit/global/110

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

N. J. A. Sloane (njas, (AT)research.att.com), Oct 26 2004