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A258294 Number of partitions of 4*n^2 into parts that are at most n. 5


%S 1,1,9,127,2280,46262,1015691,23541165,567852809,14123231487,

%T 359874480333,9351900623083,247006639629275,6613877399621729,

%U 179171447281396640,4902895256737984134,135346525073067516814,3765244155890019687101,105465364199865165010867

%N Number of partitions of 4*n^2 into parts that are at most n.

%H Vaclav Kotesovec, <a href="/A258294/b258294.txt">Table of n, a(n) for n = 0..247</a>

%F a(n) ~ c * d^n / n^2, where d = 31.379319973863251370746442877119704410889..., c = 0.0397666338404544208556554596295683858... .

%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(4*n^2, n), n=0..20);

%t (* A program to compute the constant d = 31.37931997... *) With[{j=4}, 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, A258293, A258295.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, May 25 2015

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Last modified December 6 15:23 EST 2021. Contains 349563 sequences. (Running on oeis4.)