The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002774 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002774

Number of bipartite partitions of n white objects and n black ones.
(history; published version)

#97 by Andrew Howroyd at Fri Feb 09 12:37:11 EST 2024

STATUS

reviewed

approved

#96 by Michel Marcus at Fri Feb 09 12:34:42 EST 2024

STATUS

proposed

reviewed

#95 by Michael De Vlieger at Fri Feb 09 12:13:27 EST 2024

STATUS

editing

proposed

#94 by Michael De Vlieger at Fri Feb 09 12:11:55 EST 2024

LINKS

Katherine Ormeño Bastías, Paul Martin, and Steen Ryom-Hansen, <a href="https://arxiv.org/abs/2402.01890">On the spherical partition algebra</a>, arXiv:2402.01890 [math.RT], 2024.

STATUS

approved

editing

#93 by N. J. A. Sloane at Mon Dec 20 21:16:53 EST 2021

STATUS

proposed

approved

#92 by Jon E. Schoenfield at Mon Dec 20 20:17:30 EST 2021

STATUS

editing

proposed

Discussion

Mon Dec 20

21:16

N. J. A. Sloane: If I added my name to every sequence I edited, it would be everywhere in the first 100000 entries!  So no.

#91 by Jon E. Schoenfield at Mon Dec 20 20:14:18 EST 2021

COMMENTS

Number of ways to factor p^n * q^n where p and q are distinct primes.

FORMULA

where m and n are of the same order, c = Zeta(3)^(1/3), d = Zeta(2)/(3*c) and fi(alfa) = Integral_{t=0..infinity} (1/t)*(1/(exp(alfa*t)-1)/(exp(t/alfa)-1) - (alfa/t)/(exp(alfa*t)-1) - ((1/alfa)/t)/(exp(t/alfa)-1) + 1/t^2 + (1/4)/(exp(alfa*t)-1) + (1/4)/(exp(t/alfa)-1) - (alfa/4)/t - ((1/4)/alfa)/t).

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

Discussion

Mon Dec 20

20:17

Jon E. Schoenfield: Should the 1st Extensions entry (which appeared at Revision #6) have " by _N. J. A. Sloane_" added?

#90 by N. J. A. Sloane at Sun Dec 30 21:27:22 EST 2018

STATUS

editing

approved

#89 by N. J. A. Sloane at Sun Dec 30 21:27:20 EST 2018

REFERENCES

D. E. Knuth, The Art of Computer Programming, Vol. 4A, Table A-1, see p(n,n), page 778. - N. J. A. Sloane, Dec 30 2018

CROSSREFS

Cf. A054225, also A000041, A000070, A000291, A000412, A000465, A000491, A002755, A002756, A002757, A002758, A002759, A277239.

Main diagonal of A054225 if that entry is drawn as a square array. - N. J. A. Sloane, Dec 30 2018

STATUS

approved

editing

#88 by Alois P. Heinz at Thu Oct 06 19:55:33 EDT 2016

STATUS

editing

approved