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A238000
Number of partitions of n^n into parts that are at most n.
12
0, 1, 3, 75, 123464, 33432635477, 2561606354507677872, 85980297709044488588773397089, 1841159754991692001851990839259642586671980, 34687845413783594101366282545316028561007822069601179170488
OFFSET
0,3
FORMULA
a(n) = [x^(n^n)] Product_{j=1..n} 1/(1-x^j).
a(n) ~ exp(2*n) * n^(n*(n-3)) / (2*Pi). - Vaclav Kotesovec, May 25 2015
EXAMPLE
a(1) = 1: 1.
a(2) = 3: 22, 211, 1111.
a(3) = 75: 333333333, ..., 111111111111111111111111111.
MATHEMATICA
a[n_] := SeriesCoefficient[Product[1/(1 - x^j), {j, 1, n}], {x, 0, n^n}];
a[0] = 0;
Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Nov 03 2018 *)
CROSSREFS
Main diagonal of A238010 and A238016.
Sequence in context: A336062 A320306 A359500 * A308866 A089301 A037110
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Feb 16 2014
STATUS
approved