A300975 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^3))^n.

1, 1, 3, 10, 35, 126, 462, 1716, 6443, 24391, 92928, 355862, 1368458, 5280744, 20438148, 79302960, 308385355, 1201536286, 4689450021, 18330233110, 71747534460, 281177705490, 1103163479190, 4332522733560, 17031238725410, 67007449610751, 263841039245280, 1039628691988795

Offset

0,3

Comments

Number of partitions of n into cubes 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 cubes

Formula

a(n) ~ c * d^n / sqrt(n), where d = 4.0147940395164236614815683662796167488... and c = 0.2726202310726337579308600184572222... - Vaclav Kotesovec, Mar 23 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^3*j, i-1), j=0..n/i^3)))
      end: b(n, iroot(n, 3))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Mar 17 2018

Mathematica

Table[SeriesCoefficient[Product[1/(1 - x^k^3)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]

Crossrefs

Cf. A000578, A003108, A008485, A023872, A298434, A300974.

Sequence in context: A110556 A001700 A088218 * A072266 A085282 A149036

Adjacent sequences: A300972 A300973 A300974 * A300976 A300977 A300978

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2018

Status

approved