A258295 Number of partitions of 5*n^2 into parts that are at most n.

1, 1, 11, 192, 4263, 106852, 2897747, 82966258, 2472338185, 75966810293, 2391508958235, 76782438832425, 2505642670439980, 82893573492724961, 2774547946438608789, 93807671621922558215, 3199617653993448321146, 109979504522862990517172, 3806257106793028952525938

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..230

Formula

a(n) ~ c * d^n / n^2, where d = 38.7729855097144987072847461256815071909..., c = 0.0318193213988281353709268311928... .

Maple

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

Mathematica

(* A program to compute the constant d = 38.7729855... *) With[{j=5}, 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 *)

Crossrefs

Cf. A206226, A258296, A258293, A258294.

Sequence in context: A068649 A158509 A072290 * A213691 A112127 A364942

Adjacent sequences: A258292 A258293 A258294 * A258296 A258297 A258298

Keyword

nonn

Author

Vaclav Kotesovec, May 25 2015

Status

approved