|
|
A347011
|
|
Euler transform of j-> ceiling(2^(j-2)).
|
|
2
|
|
|
1, 1, 2, 4, 9, 19, 43, 93, 207, 453, 999, 2185, 4796, 10470, 22871, 49815, 108427, 235515, 511074, 1107248, 2396299, 5179169, 11181877, 24113939, 51949572, 111801422, 240381703, 516355235, 1108186951, 2376314763, 5091422730, 10900063776, 23317805916
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Differs from A206301 first at n=10.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Product_{j>0} 1/(1-x^j)^ceiling(2^(j-2)).
|
|
MAPLE
|
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
b(n-i*j, i-1)*binomial(ceil(2^(i-2))+j-1, j), j=0..n/i)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..35);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(d*
ceil(2^(d-2)), d=numtheory[divisors](j)), j=1..n)/n)
end:
seq(a(n), n=0..35);
|
|
MATHEMATICA
|
CoefficientList[Series[1/(1-x) * Product[1/(1 - x^k)^(2^(k-2)), {k, 2, 40}], {x, 0, 40}], x] (* Vaclav Kotesovec, Aug 11 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|