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A300974 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^2))^n. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of partitions of n into squares of n kinds.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

Index entries for sequences related to partitions

Index entries for sequences related to sums of squares

FORMULA

From Vaclav Kotesovec, Mar 23 2018: (Start)

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

d = 4.216358447600641565890184638418336163396695730036... and

c = 0.26442245016754864773722176155288663999776... (End)

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

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, A300975, A301518.

Sequence in context: A149048 A149049 A149050 * A149051 A151064 A151065

Adjacent sequences:  A300971 A300972 A300973 * A300975 A300976 A300977

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 17 2018

STATUS

approved

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Last modified July 26 17:37 EDT 2021. Contains 346294 sequences. (Running on oeis4.)