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

1, 1, 9, 127, 2280, 46262, 1015691, 23541165, 567852809, 14123231487, 359874480333, 9351900623083, 247006639629275, 6613877399621729, 179171447281396640, 4902895256737984134, 135346525073067516814, 3765244155890019687101, 105465364199865165010867

Offset: 0

Author

Vaclav Kotesovec, May 25 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..247

Crossrefs

Cf. A206226, A258296, A258293, A258295.

Programs

Maple

T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n
				

Mathematica

(* 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 *)

Formula

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