The On-Line Encyclopedia of Integer Sequences (OEIS)

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A300974

a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^2))^n.
(history; published version)

#10 by Vaclav Kotesovec at Fri Mar 23 05:31:55 EDT 2018

STATUS

editing

approved

#9 by Vaclav Kotesovec at Fri Mar 23 05:30:26 EDT 2018

LINKS

Vaclav Kotesovec, <a href="/A300974/b300974.txt">Table of n, a(n) for n = 0..500</a>

FORMULA

d = 4.216358447600641565890184638418336163396695730036... and

c = 0.26442245016754864773722176155288663999776... (End)

#8 by Vaclav Kotesovec at Fri Mar 23 05:23:54 EDT 2018

FORMULA

From Vaclav Kotesovec, Mar 23 2018: (Start)

a(n) ~ c * d^n / sqrt(n), where

d = 4.216358447600641565890184638418336163396695730036... and

c = 0.26442245016754864773722176155288663999776... (End)

#7 by Vaclav Kotesovec at Fri Mar 23 05:17:12 EDT 2018

CROSSREFS

Cf. A000290, A001156, A008485, A023871, A240944, A279225, A285047, A300975, A301518.

STATUS

approved

editing

#6 by Alois P. Heinz at Sat Mar 17 13:45:54 EDT 2018

STATUS

editing

approved

#5 by Alois P. Heinz at Sat Mar 17 13:45:36 EDT 2018

MAPLE

a:= proc(m) option remember; local b; b:= proc(n, i)

option remember; `if`(n=0, 1, `if`(i<1, 0, add(

binomial(m+j-1, j)*b(n-i^2*j, i-1), j=0..n/i^2)))

end: b(n, isqrt(n))

end:

seq(a(n), n=0..30); # Alois P. Heinz, Mar 17 2018

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Sat Mar 17 09:48:45 EDT 2018

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Sat Mar 17 08:43:16 EDT 2018

CROSSREFS

Cf. A000290, A001156, A008485, A023871, A240944, A279225, A285047, A300975.

#2 by Ilya Gutkovskiy at Sat Mar 17 08:38:21 EDT 2018

NAME

allocated for Ilya Gutkovskiy

a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^2))^n.

DATA

1, 1, 3, 10, 39, 151, 588, 2304, 9111, 36307, 145553, 586246, 2370264, 9614242, 39105580, 159444160, 651468967, 2666771488, 10934393619, 44899828056, 184616878289, 760010818689, 3132147583744, 12921037206764, 53351800567200, 220478125956426, 911839751015196, 3773836780169050

OFFSET

0,3

COMMENTS

Number of partitions of n into squares of n kinds.

LINKS

<a href="/index/Par#part">Index entries for sequences related to partitions</a>

<a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

MATHEMATICA

Table[SeriesCoefficient[Product[1/(1 - x^k^2)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

CROSSREFS

Cf. A000290, A001156, A008485, A023871, A240944, A279225, A285047.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Mar 17 2018

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sat Mar 17 08:38:21 EDT 2018

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved