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A238608 Number of partitions of n^3 into parts that are at most n. 13
1, 1, 5, 75, 2280, 106852, 6889527, 569704489, 57733506640, 6944433285769, 968356321790171, 153738253618009045, 27396489338187214000, 5417302365503826145732, 1177436831956414016252071, 279074576444362385794783853, 71649589941044468875380333533 (list; graph; refs; listen; history; text; internal format)
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 01 2014
STATUS
approved

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Last modified February 23 01:10 EST 2024. Contains 370265 sequences. (Running on oeis4.)