A258294 Number of partitions of 4*n^2 into parts that are at most n.

1, 1, 9, 127, 2280, 46262, 1015691, 23541165, 567852809, 14123231487, 359874480333, 9351900623083, 247006639629275, 6613877399621729, 179171447281396640, 4902895256737984134, 135346525073067516814, 3765244155890019687101, 105465364199865165010867

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: A034301 A092651 A366036 * A362776 A365033 A073014

Adjacent sequences: A258291 A258292 A258293 * A258295 A258296 A258297

Keyword

nonn

Author

Vaclav Kotesovec, May 25 2015

Status

approved