A347011 Euler transform of j-> ceiling(2^(j-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

Offset: 0

Author

Alois P. Heinz, Aug 10 2021

Keywords

• nonn

Comments

Differs from A206301 first at n=10.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3250

Crossrefs

Cf. A034691, A034899, A166861, A187251, A206301, A319918.

Programs

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 *)

Formula

G.f.: Product_{j>0} 1/(1-x^j)^ceiling(2^(j-2)).