|
|
A349113
|
|
a(n) = 8^n * P(3*n, n), where P(n, x) is n-th Legendre polynomial.
|
|
2
|
|
|
1, 8, 40636, 748832256, 37759888297756, 4086692369433395200, 815254385427670754825764, 270587150855247020644760551424, 138859707622050969870951620062449436, 104286590422721059977069662227099300134912, 109828573459404650800550127862919905133973562480
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
In general, for k>=1, P(k*n, n) ~ 2^(k*n) * n^(k*n) / sqrt(k*Pi*n).
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 2^(6*n) * n^(3*n - 1/2) / sqrt(3*Pi).
|
|
MATHEMATICA
|
Table[8^n*LegendreP[3*n, n], {n, 0, 12}]
|
|
PROG
|
(PARI) a(n) = 8^n*pollegendre(3*n, n); \\ Michel Marcus, Nov 08 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|