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%I #11 Jun 11 2015 05:13:31
%S 1,1,5,37,351,3765,43752,536375,6842599,89984614,1212199424,
%T 16651935901,232477235048,3290090540717,47106320777132,
%U 681247106742555,9938641464083052,146113228303254020,2162784490438698636,32209221982817148364,482304350308369699381
%N Number of partitions of 2*n^2 into parts that are at most n.
%H Vaclav Kotesovec, <a href="/A258296/b258296.txt">Table of n, a(n) for n = 0..307</a>
%F a(n) ~ c * d^n / n^2, where d = 16.57962120993269533568313969522872808998..., c = 0.07942450354657307077058855728600800998... .
%p T:=proc(n,k) option remember; `if`(n=0 or k=1, 1, T(n,k-1) + `if`(n<k, 0, T(n-k,k))) end proc: seq(T(2*n^2, n), n=0..20);
%t (* A program to compute the constant d = 16.5796212... *) With[{j=2}, r^(2*j+1)/(r-1) /.FindRoot[-PolyLog[2,1-r] == (j+1/2)*Log[r]^2, {r, E}, WorkingPrecision->100]] (* _Vaclav Kotesovec_, Jun 10 2015 *)
%Y Cf. A206226, A258293, A258294, A258295.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 25 2015
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