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A161408
Number of partitions of n^2 into parts greater than n.
5
1, 0, 1, 2, 6, 17, 56, 179, 607, 2076, 7269, 25736, 92360, 334506, 1222463, 4499892, 16673446, 62130710, 232700539, 875483029, 3307244256, 12539455600, 47702381244, 182021195608, 696487788847, 2671877845634, 10274126646175, 39593295985708, 152889766657797
OFFSET
0,4
LINKS
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 4.076293... and c = 0.187307... - Vaclav Kotesovec, Sep 08 2021
EXAMPLE
a(4) = #{16, 11+5, 10+6, 9+7, 8+8, 6+5+5} = 6.
MAPLE
a := proc (n) local G, Gser: G := 1/(product(1-x^j, j = n+1 .. n^2)): Gser := series(G, x = 0, n^2+5): coeff(Gser, x, n^2) end proc: 1, seq(a(n), n = 1 .. 27); # Emeric Deutsch, Jun 22 2009
MATHEMATICA
a[n_] := a[n] = 1/Product[1 - x^j, {j, n + 1, n^2}] + O[x]^(n^2 + 1) // CoefficientList[#, x]& // Last;
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 28}] (* Jean-François Alcover, May 18 2017, adapted from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 10 2009
EXTENSIONS
Extended by Emeric Deutsch, Jun 22 2009
a(0)=1 from Alois P. Heinz, Dec 21 2014
STATUS
approved