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A258293 Number of partitions of 3*n^2 into parts that are at most n. 5
1, 1, 7, 75, 1033, 16019, 269005, 4767088, 87914929, 1671580383, 32560379840, 646795901962, 13058489343812, 267268692575830, 5534279506641422, 115754904055926892, 2442438538492842691, 51934447672016653655, 1111872048730513043539, 23949840661000275507964 (list; graph; refs; listen; history; text; internal format)
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: A197763 A202251 A243692 * A127190 A121316 A220215

Adjacent sequences:  A258290 A258291 A258292 * A258294 A258295 A258296

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 25 2015

STATUS

approved

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Last modified December 7 07:01 EST 2021. Contains 349567 sequences. (Running on oeis4.)