The On-Line Encyclopedia of Integer Sequences (OEIS)

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A298598

Expansion of Product_{k>=2} (1 + x^k)^k.
(history; published version)

#10 by Vaclav Kotesovec at Tue Dec 08 11:40:03 EST 2020

STATUS

reviewed

approved

#9 by Michel Marcus at Tue Dec 08 11:26:28 EST 2020

STATUS

proposed

reviewed

#8 by Seiichi Manyama at Tue Dec 08 11:26:13 EST 2020

STATUS

editing

proposed

#7 by Seiichi Manyama at Tue Dec 08 11:24:51 EST 2020

LINKS

Seiichi Manyama, <a href="/A298598/b298598.txt">Table of n, a(n) for n = 0..10000</a>

STATUS

approved

editing

#6 by Vaclav Kotesovec at Sun Apr 08 06:32:46 EDT 2018

STATUS

editing

approved

#5 by Vaclav Kotesovec at Sun Apr 08 06:31:14 EDT 2018

FORMULA

From Vaclav Kotesovec, Apr 08 2018: (Start)

a(n) + a(n+1) = A026007(n+1).

a(n) ~ Zeta(3)^(1/6) * exp((3/2)^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(7/4) * 3^(1/3) * sqrt(Pi) * n^(2/3)). (End)

STATUS

approved

editing

#4 by N. J. A. Sloane at Mon Jan 22 18:41:57 EST 2018

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Mon Jan 22 14:32:21 EST 2018

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Mon Jan 22 13:24:26 EST 2018

NAME

allocated for Ilya Gutkovskiy

Expansion of Product_{k>=2} (1 + x^k)^k.

DATA

1, 0, 2, 3, 5, 11, 17, 32, 51, 91, 144, 241, 386, 618, 981, 1540, 2400, 3711, 5710, 8699, 13217, 19917, 29891, 44593, 66244, 97888, 144072, 211097, 308061, 447833, 648578, 935941, 1345985, 1929291, 2756440, 3926259, 5575720, 7895519, 11149261, 15701660, 22054901, 30900798, 43188113

OFFSET

0,3

COMMENTS

Number of partitions of n into distinct parts > 1, where n different parts of size n (beginning at 2) are available (2a, 2b, 3a, 3b, 3c, 4a, 4b, 4c, 4d, ...).

Convolution of the sequences A026007 and A033999.

LINKS

<a href="/index/Par#part">Index entries for related partition-counting sequences</a>

FORMULA

G.f.: Product_{k>=2} (1 + x^k)^k.

MATHEMATICA

nmax = 42; CoefficientList[Series[Product[(1 + x^k)^k, {k, 2, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A025147, A026007, A191659.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Jan 22 2018

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Jan 22 13:24:26 EST 2018

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved