The On-Line Encyclopedia of Integer Sequences (OEIS)

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A341388

Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^6.
(history; published version)

#9 by Alois P. Heinz at Wed Feb 10 18:50:41 EST 2021

STATUS

editing

approved

#8 by Alois P. Heinz at Wed Feb 10 18:49:59 EST 2021

LINKS

Alois P. Heinz, <a href="/A341388/b341388.txt">Table of n, a(n) for n = 6..10000</a>

STATUS

approved

editing

#7 by Bruno Berselli at Wed Feb 10 15:01:30 EST 2021

STATUS

proposed

approved

#6 by Alois P. Heinz at Wed Feb 10 14:53:04 EST 2021

STATUS

editing

proposed

#5 by Alois P. Heinz at Wed Feb 10 14:53:01 EST 2021

MAPLE

g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(d^2/

`if`(d::odd, 1, 2), d=numtheory[divisors](j)), j=1..n)/n)

end:

b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0,

g(n)), (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))

end:

a:= n-> b(n, 6):

seq(a(n), n=6..30); # Alois P. Heinz, Feb 10 2021

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Wed Feb 10 14:38:06 EST 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Wed Feb 10 14:07:13 EST 2021

CROSSREFS

Cf. A026007, A321951, A327384, A341384, A341385, A341386, A341387, A341390, A341391.

#2 by Ilya Gutkovskiy at Wed Feb 10 13:56:39 EST 2021

NAME

allocated for Ilya Gutkovskiy

Expansion of (-1 + Product_{k>=1} (1 + x^k)^k)^6.

DATA

1, 12, 90, 508, 2391, 9840, 36578, 125358, 402093, 1220232, 3532836, 9821280, 26352110, 68528718, 173311971, 427486178, 1030855416, 2435255634, 5645810201, 12864839166, 28850671284, 63751119334, 138946592610, 298974483954, 635626314025

OFFSET

6,2

MATHEMATICA

nmax = 30; CoefficientList[Series[(-1 + Product[(1 + x^k)^k, {k, 1, nmax}])^6, {x, 0, nmax}], x] // Drop[#, 6] &

CROSSREFS

Cf. A026007, A321951, A327384.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Feb 10 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Wed Feb 10 13:56:39 EST 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved