|
|
A281245
|
|
Expansion of Product_{k>=1} (1 + x^(7*k-1)).
|
|
15
|
|
|
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 2, 3, 1, 0, 0, 0, 0, 3, 4, 1, 0, 0, 0, 1, 4, 4, 1, 0, 0, 0, 1, 5, 5, 1, 0, 0, 0, 2, 7, 5, 1, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,34
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ exp(sqrt(n/21)*Pi) / (2^(13/7)*21^(1/4)*n^(3/4)) * (1 + (13*Pi/(336*sqrt(21)) - 3*sqrt(21)/(8*Pi)) / sqrt(n)). - Vaclav Kotesovec, Jan 18 2017, extended Jan 24 2017
G.f.: Sum_{k>=0} x^(k*(7*k + 5)/2) / Product_{j=1..k} (1 - x^(7*j)). - Ilya Gutkovskiy, Nov 24 2020
|
|
MATHEMATICA
|
nmax = 200; CoefficientList[Series[Product[(1 + x^(7*k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 200; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 7] == 6, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|