The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A099706 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A099706

Consider the family of directed multigraphs enriched by the species of directed graphs. 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 21:32:02 EST 2021

STATUS

proposed

approved

#11 by Andrew Howroyd at Tue Jan 12 21:16:23 EST 2021

STATUS

editing

proposed

#10 by Andrew Howroyd at Tue Jan 12 20:38:38 EST 2021

NAME

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

DATA

1, 4, 84, 3568, 305712, 87782720, 144600947392, 1139235294403328, 37012349010095737088, 4840037457225169875031040, 2535930555678883610642223895552, 5317274645187046706095607711946092544, 44602319906972740832371696997145322907873280

LINKS

Andrew Howroyd, <a href="/A099706/b099706.txt">Table of n, a(n) for n = 0..50</a>

FORMULA

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A002416. - Andrew Howroyd, Jan 12 2021

PROG

(PARI) \\ R(n) is A002416 as e.g.f.; EnrichedGdlSeq defined in A098622.

R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)}

EnrichedGdlSeq(R(15)) \\ Andrew Howroyd, Jan 12 2021

CROSSREFS

Cf. A002416, A014507, A098622, A099704, A099705, A099707.

EXTENSIONS

Terms a(10) and beyond from Andrew Howroyd, Jan 12 2021

STATUS

approved

editing

#9 by N. J. A. Sloane at Sun Jun 25 15:17:38 EDT 2017

STATUS

editing

approved

#8 by N. J. A. Sloane at Sun Jun 25 15:17:34 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 06:48:13 EDT 2015

STATUS

editing

approved

#6 by Jon E. Schoenfield at Fri Oct 23 06:48:10 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