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A126391 a(1)=1; for n>1: a(n) = sum of all subsets of (a(1),..,a(n-1)).

%I A126391 #5 Jun 25 2022 22:52:52
%S A126391 1,1,4,24,240,4320,146880,9694080,1260230400,325139443200,
%T A126391 167121673804800,171466837323724800,351507016513635840000,
%U A126391 1440475753672879672320000,11803258325595576034990080000
%N A126391 a(1)=1; for n>1: a(n) = sum of all subsets of (a(1),..,a(n-1)).
%C A126391 Is connection with A006088 clear?
%C A126391 Apparently first differences of A028361. - _Sean A. Irvine_, Jun 25 2022
%F A126391 a(1)=1, a(2)=1; n>2: a(n)=(2^(n-2)+2)*a(n-1). a(1)=1; n>1: a(n)=A006088(n-1).
%e A126391 n=2: subsets of (1) are ((0),(1)), sums of subsets are (0,1) and total sum is 0+1=1, hence a(2)=1;
%e A126391 n=3: subsets of (1,1) are ((0),(1),(1),(1,1)), sums of subsets are (0,1,1,2) and total sum is 0+1+1+2=4, hence a(3)=4;
%e A126391 n=4: subsets of (1,1,4) are ((0),(1),(1),(4),(1,1),(1,4),(1,4),(1,1,4)), sums of subsets are (0,1,1,4,2,5,5,6) and total sum is 0+1+1+4+2+5+5+6=24, hence a(4)=24.
%t A126391 a[1]=1;a[2]=1;a[n_]:=a[n]=(2^(n-2)+2)*a[n-1];Table[a[i],{i,18}]
%Y A126391 Cf. A006088.
%K A126391 nonn
%O A126391 1,3
%A A126391 _Zak Seidov_, Mar 23 2007