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

0,4

Links

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

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

Cf. A072213, A093116, A161407.

Sequence in context: A097514 A108630 A338735 * A150033 A150034 A238127

Adjacent sequences: A161405 A161406 A161407 * A161409 A161410 A161411

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