|
|
A258798
|
|
a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^k.
|
|
2
|
|
|
1, 3, 12, 62, 327, 1851, 10802, 64440, 391218, 2408001, 14989608, 94197594, 596756374, 3807010920, 24435261432, 157681777148, 1022391454116, 6657413851086, 43517229086467, 285447137446989, 1878287880309900, 12395149957521672, 82014499806039711
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c * d^n / n^(3/2), where d = 7.036711302278424796297167109247361745558645910729132828752853658917..., c = 2.3254811458... .
|
|
MATHEMATICA
|
Table[SeriesCoefficient[Product[(1+x^k)^3/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+3)/2}], {n, 0, 30}]
(* A program to compute the constant d *) (1+r)^3/r^2 /.FindRoot[-Pi^2/12 - Log[r]^2/3 + 1/2*Log[1+r]^2 + PolyLog[2, 1/(1+r)] == 0, {r, E}, WorkingPrecision->100]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|