The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A362610 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A362610

Number of integer partitions of n having a unique part of least multiplicity.
(history; published version)

#14 by OEIS Server at Thu May 04 14:57:22 EDT 2023

LINKS

Andrew Howroyd, <a href="/A362610/b362610_1.txt">Table of n, a(n) for n = 0..1000</a>

#13 by Michael De Vlieger at Thu May 04 14:57:22 EDT 2023

STATUS

proposed

approved

Discussion

Thu May 04

14:57

OEIS Server: Installed first b-file as b362610.txt.

#12 by Andrew Howroyd at Thu May 04 12:13:20 EDT 2023

STATUS

editing

proposed

#11 by Andrew Howroyd at Thu May 04 12:13:14 EDT 2023

FORMULA

G.f.: Sum_{m>=2} (Sum_{j>=1} x^(j*(m-1))/(1 + x^(j*m)/(1 - x^j))) * (Product_{j>=1} (1 + x^(j*m)/(1 - x^j))). - Andrew Howroyd, May 04 2023

STATUS

proposed

editing

#10 by Andrew Howroyd at Thu May 04 12:02:40 EDT 2023

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editing

proposed

#9 by Andrew Howroyd at Thu May 04 12:01:16 EDT 2023

LINKS

Andrew Howroyd, <a href="/A362610/b362610_1.txt">Table of n, a(n) for n = 0..1000</a>

PROG

(PARI) seq(n) = my(A=O(x*x^n)); Vec(sum(m=2, n+1, sum(j=1, n, x^(j*(m-1))/(1 + if(j*m<=n, x^(j*m)/(1-x^j) )) + A)*prod(j=1, n\m, 1 + x^(j*m)/(1 - x^j) + A)), -(n+1)) \\ Andrew Howroyd, May 04 2023

STATUS

approved

editing

#8 by Michael De Vlieger at Tue May 02 16:07:51 EDT 2023

STATUS

proposed

approved

#7 by Gus Wiseman at Tue May 02 14:59:32 EDT 2023

STATUS

editing

proposed

#6 by Gus Wiseman at Tue May 02 14:59:00 EDT 2023

COMMENTS

Alternatively, these are partitions with a part appearing fewer times than any othereach of the others.

CROSSREFS

Cf. A008284, A053263, A098859, A237984, A240219, A304442, A327472, A353863, A353864, A353865, `A360071, `A360687, A362612.

#5 by Gus Wiseman at Tue May 02 14:27:45 EDT 2023

CROSSREFS

For parts instead of multiplicities we have A002865, ranks A247180.