A258296 Number of partitions of 2*n^2 into parts that are at most n.

1, 1, 5, 37, 351, 3765, 43752, 536375, 6842599, 89984614, 1212199424, 16651935901, 232477235048, 3290090540717, 47106320777132, 681247106742555, 9938641464083052, 146113228303254020, 2162784490438698636, 32209221982817148364, 482304350308369699381

Offset: 0

Author

Vaclav Kotesovec, May 25 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..307

Crossrefs

Cf. A206226, A258293, A258294, 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 = 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 *)

Formula

a(n) ~ c * d^n / n^2, where d = 16.57962120993269533568313969522872808998..., c = 0.07942450354657307077058855728600800998... .