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%I #12 Jun 11 2015 05:12:57
%S 1,1,7,75,1033,16019,269005,4767088,87914929,1671580383,32560379840,
%T 646795901962,13058489343812,267268692575830,5534279506641422,
%U 115754904055926892,2442438538492842691,51934447672016653655,1111872048730513043539,23949840661000275507964
%N Number of partitions of 3*n^2 into parts that are at most n.
%H Vaclav Kotesovec, <a href="/A258293/b258293.txt">Table of n, a(n) for n = 0..274</a>
%F a(n) ~ c * d^n / n^2, where d = 23.98280768122086592445663786762351573848..., c = 0.0530017980244665552354063060738409813... .
%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(3*n^2, n), n=0..20);
%t (* A program to compute the constant d = 23.98280768... *) With[{j=3}, 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, A258296, A258294, A258295.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, May 25 2015
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