A258293 Number of partitions of 3*n^2 into parts that are at most n.

1, 1, 7, 75, 1033, 16019, 269005, 4767088, 87914929, 1671580383, 32560379840, 646795901962, 13058489343812, 267268692575830, 5534279506641422, 115754904055926892, 2442438538492842691, 51934447672016653655, 1111872048730513043539, 23949840661000275507964

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..274

Formula

a(n) ~ c * d^n / n^2, where d = 23.98280768122086592445663786762351573848..., c = 0.0530017980244665552354063060738409813... .

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

Mathematica

(* 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 *)

Crossrefs

Cf. A206226, A258296, A258294, A258295.

Sequence in context: A202251 A365841 A243692 * A127190 A121316 A220215

Adjacent sequences: A258290 A258291 A258292 * A258294 A258295 A258296

Keyword

nonn

Author

Vaclav Kotesovec, May 25 2015

Status

approved