The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A174467 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A174467

G.f.: exp( Sum_{n>=1} A174468(n)*x^n/n ) where A174468(n) = Sum_{d|n} d*sigma(n/d)*sigma(d).
(history; published version)

#13 by Andrew Howroyd at Mon Sep 30 21:16:48 EDT 2024

STATUS

proposed

approved

#12 by Mark Daniel Ward at Mon Sep 30 21:16:02 EDT 2024

STATUS

editing

proposed

#11 by Mark Daniel Ward at Mon Sep 30 21:15:39 EDT 2024

LINKS

Lida Ahmadi, Ricardo Gómez Aíza, and Mark Daniel Ward, <a href="https://arxivdoi.org/abs/230310.022401007/s44007-024-00134-w">A unified treatment of families of partition functions</a>, La Matematica (2024). Preprint available as <a href="https://arxiv.org/abs/2303.02240">arXiv:2303.02240 </a> [math.CO], 2023.

STATUS

approved

editing

Discussion

Mon Sep 30

21:16

Mark Daniel Ward: The exact same edit was just approved for these sixteen sequences: A026007, A107742, A061256, A028342, A192065, A280540, A280486, A280473, A280541, A168243, A318413, A318414, A318696, A305127, A318769, A318695.  We hope that this edit is acceptable too.

#10 by N. J. A. Sloane at Thu Feb 29 20:43:37 EST 2024

FORMULA

From _Ricardo Gomez_, Gómez Aíza_, Mar 08 2023: (Start)

Discussion

Thu Feb 29

20:43

OEIS Server: https://oeis.org/edit/global/2981

#9 by Michael De Vlieger at Fri Mar 10 10:07:57 EST 2023

STATUS

proposed

approved

#8 by Michael De Vlieger at Fri Mar 10 10:07:49 EST 2023

STATUS

editing

proposed

#7 by Michael De Vlieger at Fri Mar 10 10:07:37 EST 2023

LINKS

L. Lida Ahmadi, R. Ricardo Gómez Aíza, and M. D. Mark Daniel Ward. , <a href="https://arxiv.org/abs/2303.02240">A unified treatment of families of partition functions</a>, arXiv:2303.02240 [math.CO], 2023.

#6 by Jon E. Schoenfield at Thu Mar 09 05:06:53 EST 2023

FORMULA

log(a(n) / n!) ~ (3 / 2) * (Zeta(3) * Pi ^ 4 / 18) ^(1 / 3) * n ^(2 / 3). (End)

#5 by Jon E. Schoenfield at Thu Mar 09 05:04:31 EST 2023

FORMULA

E.g.f.: Prod_Product_{n>=1,m>=1,k>=1} 1 / (1 - x^(n * m * k))^n.

#4 by Joerg Arndt at Thu Mar 09 02:25:48 EST 2023

FORMULA

From Ricardo Gomez, Mar 08 2023: (Start)

GE.g.f.: Sum_{n >= 0} (a(n) / n!) x ^n = Prod_{n>=1,m>=1,k>=1} 1 / (1 - x^{(n * m * k}) )^ n.

log(a(n) / n!) ~ (3 / 2) * (Zeta(3) * Pi ^ 4 / 18) ^(1 / 3) * n ^(2 / 3). _Ricardo Gomez_, Mar 08 2023(End)