The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A098638 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A098638

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

#15 by N. J. A. Sloane at Tue Jan 12 21:30:41 EST 2021

STATUS

proposed

approved

#14 by Andrew Howroyd at Tue Jan 12 21:15:43 EST 2021

STATUS

editing

proposed

#13 by Andrew Howroyd at Tue Jan 12 20:08:18 EST 2021

NAME

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

DATA

1, 2, 13, 164, 3127, 82600, 2845775, 122820136, 6446913953, 402413160952, 29343933156485, 2464029760993520, 235446319553848087, 25346231173047308256, 3047931031445529965527, 406412844141860523543392, 59704680455100785101683457, 9608818815170839730520275488

LINKS

Andrew Howroyd, <a href="/A098638/b098638.txt">Table of n, a(n) for n = 0..200</a>

FORMULA

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

PROG

(PARI) \\ EnrichedGdlSeq defined in A098622.

EnrichedGdlSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021

CROSSREFS

Cf. A014507, A098622, A098636, A098637, A098639.

EXTENSIONS

Missing a(10) inserted and terms a(13) and beyond from Andrew Howroyd, Jan 12 2021

STATUS

approved

editing

#12 by N. J. A. Sloane at Sun Jun 25 15:07:13 EDT 2017

STATUS

editing

approved

#11 by N. J. A. Sloane at Sun Jun 25 15:07:10 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

#10 by Jon E. Schoenfield at Fri Oct 23 06:57:08 EDT 2015

STATUS

editing

approved

#9 by Jon E. Schoenfield at Fri Oct 23 06:57:06 EDT 2015

REFERENCES

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

FORMULA

E.g.f.: exp(-1)*sum(Sum_{n>=0}(1+sinh(x))^(n^2)/n!,n = 0 .. infinity). - Vladeta Jovovic, Mar 04 2008

STATUS

approved

editing

#8 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

#7 by Charles R Greathouse IV at Fri May 10 12:45:37 EDT 2013

FORMULA

E.g.f.: exp(-1)*sum((1+sinh(x))^(n^2)/n!,n = 0 .. infinity). - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Mar 04 2008

Discussion

Fri May 10

12:45

OEIS Server: https://oeis.org/edit/global/1911

#6 by Russ Cox at Fri Mar 30 16:50:03 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