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%I #17 Jun 30 2022 08:40:46
%S 0,2,20,328,10512,672800,86118464,22046326912,11287719379200,
%T 11558624644301312,23672063271529088000,96960771160183144450048,
%U 794302637344220319334797312,13013854410247705711981319168000,426437981314996820770203866497040384
%N Convert the binary strings in A101305 to decimal.
%C The a(n)-th composition in standard order is (2,3,..,n+1), where the k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. Moreover, the binary indices of a(n) are row n of A193973. Including 1 gives A164894, reverse A246534. - _Gus Wiseman_, Jun 28 2022
%H Michael S. Branicky, <a href="/A104462/b104462.txt">Table of n, a(n) for n = 0..80</a>
%e From _Gus Wiseman_, Jun 28 2022: (Start)
%e The terms together with their standard compositions begin:
%e 0: ()
%e 2: (2)
%e 20: (2,3)
%e 328: (2,3,4)
%e 10512: (2,3,4,5)
%e (End)
%p convert(10,decimal,binary); convert(10100,decimal,binary); convert(101001000,decimal,binary); convert(10100100010000,decimal,binary); convert(10100100010000100000,decimal,binary);
%t stcinv[q_]:=Total[2^Accumulate[Reverse[q]]]/2;
%t Table[stcinv[Range[2,n]],{n,8}] (* _Gus Wiseman_, Jun 28 2022 *)
%o (Python)
%o def a(n): return 0 if n==0 else int("".join("1"+"0"*(i+1) for i in range(n)), 2)
%o print([a(n) for n in range(15)]) # _Michael S. Branicky_, Jun 28 2022
%Y Cf. A101305.
%Y A version for prime indices is A070826.
%Y Cf. A000120, A002110, A029931, A066099, A070939, A164894, A193973, A233564, A246534, A272919, A333218, A333255.
%K nonn,base
%O 0,2
%A _Jorge Coveiro_, Apr 23 2005
%E a(14) and beyond from _Michael S. Branicky_, Jun 28 2022
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