|
|
A336242
|
|
a(n) = (n!)^2 * Sum_{d|n} (-1)^(d+1) / (d!)^2.
|
|
1
|
|
|
1, 3, 37, 431, 14401, 403199, 25401601, 1216454399, 135339724801, 9877056537599, 1593350922240001, 178056522962841599, 38775788043632640001, 5700041141609893478399, 1757631343928533032960001, 327562346808114783805439999, 126513546505547170185216000001
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (n!)^2 * [x^n] Sum_{k>=1} (1 - BesselJ(0,2*x^(k/2))).
a(n) = (n!)^2 * [x^n] Sum_{k>=1} -(-x)^k / ((k!)^2 * (1 - x^k)).
|
|
MATHEMATICA
|
Table[(n!)^2 Sum[(-1)^(d + 1)/(d!)^2, {d, Divisors[n]}], {n, 1, 17}]
nmax = 17; CoefficientList[Series[Sum[(1 - BesselJ[0, 2 x^(k/2)]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2 // Rest
|
|
PROG
|
(PARI) a(n) = n!^2*sumdiv(n, d, (-1)^(d+1)/d!^2); \\ Michel Marcus, Jul 13 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|