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A258295 Number of partitions of 5*n^2 into parts that are at most n. 5
1, 1, 11, 192, 4263, 106852, 2897747, 82966258, 2472338185, 75966810293, 2391508958235, 76782438832425, 2505642670439980, 82893573492724961, 2774547946438608789, 93807671621922558215, 3199617653993448321146, 109979504522862990517172, 3806257106793028952525938 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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
Sequence in context: A068649 A158509 A072290 * A213691 A112127 A364942
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 25 2015
STATUS
approved

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Last modified March 2 10:43 EST 2024. Contains 370466 sequences. (Running on oeis4.)