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%I #14 Sep 08 2021 07:12:40
%S 1,0,1,2,6,17,56,179,607,2076,7269,25736,92360,334506,1222463,4499892,
%T 16673446,62130710,232700539,875483029,3307244256,12539455600,
%U 47702381244,182021195608,696487788847,2671877845634,10274126646175,39593295985708,152889766657797
%N Number of partitions of n^2 into parts greater than n.
%H Seiichi Manyama, <a href="/A161408/b161408.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) ~ c * d^n / n^(3/2), where d = 4.076293... and c = 0.187307... - _Vaclav Kotesovec_, Sep 08 2021
%e a(4) = #{16, 11+5, 10+6, 9+7, 8+8, 6+5+5} = 6.
%p 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
%t a[n_] := a[n] = 1/Product[1 - x^j, {j, n + 1, n^2}] + O[x]^(n^2 + 1) // CoefficientList[#, x]& // Last;
%t Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 28}] (* _Jean-François Alcover_, May 18 2017, adapted from Maple *)
%Y Cf. A072213, A093116, A161407.
%K nonn
%O 0,4
%A _Reinhard Zumkeller_, Jun 10 2009
%E Extended by _Emeric Deutsch_, Jun 22 2009
%E a(0)=1 from _Alois P. Heinz_, Dec 21 2014
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