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

%I A347011 #16 Aug 11 2021 05:30:58
%S A347011 1,1,2,4,9,19,43,93,207,453,999,2185,4796,10470,22871,49815,108427,
%T A347011 235515,511074,1107248,2396299,5179169,11181877,24113939,51949572,
%U A347011 111801422,240381703,516355235,1108186951,2376314763,5091422730,10900063776,23317805916
%N A347011 Euler transform of j-> ceiling(2^(j-2)).
%C A347011 Differs from A206301 first at n=10.
%H A347011 Alois P. Heinz, <a href="/A347011/b347011.txt">Table of n, a(n) for n = 0..3250</a>
%F A347011 G.f.: Product_{j>0} 1/(1-x^j)^ceiling(2^(j-2)).
%p A347011 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
%p A347011       b(n-i*j, i-1)*binomial(ceil(2^(i-2))+j-1, j), j=0..n/i)))
%p A347011     end:
%p A347011 a:= n-> b(n$2):
%p A347011 seq(a(n), n=0..35);
%p A347011 # second Maple program:
%p A347011 a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(d*
%p A347011        ceil(2^(d-2)), d=numtheory[divisors](j)), j=1..n)/n)
%p A347011     end:
%p A347011 seq(a(n), n=0..35);
%t A347011 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 *)
%Y A347011 Cf. A034691, A034899, A166861, A187251, A206301, A319918.
%K A347011 nonn
%O A347011 0,3
%A A347011 _Alois P. Heinz_, Aug 10 2021