A238608 Number of partitions of n^3 into parts that are at most n.

1, 1, 5, 75, 2280, 106852, 6889527, 569704489, 57733506640, 6944433285769, 968356321790171, 153738253618009045, 27396489338187214000, 5417302365503826145732, 1177436831956414016252071, 279074576444362385794783853, 71649589941044468875380333533

Offset

0,3

Comments

In general, "number of partitions of j*n^3 into parts that are at most n" is (for j>0) asymptotic to exp(2*n + 1/(4*j)) * n^(n-3) * j^(n-1) / (2*Pi). - Vaclav Kotesovec, May 25 2015

Links

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..122 (terms 0..70 from Alois P. Heinz)

Formula

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

a(n) ~ exp(2*n + 1/4) * n^(n-3) / (2*Pi). - Vaclav Kotesovec, May 25 2015

Maple

T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n<k, 0, T(n-k, k))) end proc: seq(T(n^3, n), n=0..20); # Vaclav Kotesovec, May 25 2015 after Alois P. Heinz

Mathematica

a[n_] := SeriesCoefficient[1/QPochhammer[q, q, n], {q, 0, n^3}]; Table[ a[n], {n, 0, 20}] (* Jean-François Alcover, Dec 03 2015 *)

Crossrefs

Column k=3 of A238016.

Cf. A258302 (j=2), A258303 (j=3), A258304 (j=4), A258305 (j=5).

Sequence in context: A219462 A091882 A034688 * A132855 A238560 A303125

Adjacent sequences: A238605 A238606 A238607 * A238609 A238610 A238611

Keyword

nonn

Author

Alois P. Heinz, Mar 01 2014

Status

approved