A161408 Number of partitions of n^2 into parts greater than n.

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

Author

Reinhard Zumkeller, Jun 10 2009

Keywords

• nonn

Examples

			a(4) = #{16, 11+5, 10+6, 9+7, 8+8, 6+5+5} = 6.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A072213, A093116, A161407.

Programs

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 *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = 4.076293... and c = 0.187307... - Vaclav Kotesovec, Sep 08 2021

Extensions

Extended by Emeric Deutsch, Jun 22 2009

a(0)=1 from Alois P. Heinz, Dec 21 2014