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A258294 Number of partitions of 4*n^2 into parts that are at most n. 5
1, 1, 9, 127, 2280, 46262, 1015691, 23541165, 567852809, 14123231487, 359874480333, 9351900623083, 247006639629275, 6613877399621729, 179171447281396640, 4902895256737984134, 135346525073067516814, 3765244155890019687101, 105465364199865165010867 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

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

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 *)

CROSSREFS

Cf. A206226, A258296, A258293, A258295.

Sequence in context: A338077 A034301 A092651 * A073014 A046754 A203425

Adjacent sequences:  A258291 A258292 A258293 * A258295 A258296 A258297

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 25 2015

STATUS

approved

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Last modified October 27 15:27 EDT 2021. Contains 348287 sequences. (Running on oeis4.)