%I A157904
%S A157904 1,2,4,8,17,36,78,170,375,833,1870,4229,9654,22223,51622,120961,286029,
%T A157904 682398,1642821,3990231,9777678,24166327,60233185,151350709,383287499,
%U A157904 977918150,2512805727,6500178867,16921248231,44310852884,116678914575
%N A157904 INVERT transform of A000055
%F A157904 INVERT transform of A000055: (1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106,...).
%e A157904 a(3) = 8 = (1, 1, 1) dot (1, 2, 4) + 1 = 7 + 1 = 8; where the operation 
               uses ascending terms of A000055: (1, 1, 1, 1, 2, 3, 6, 11,...) and 
               an equal number of ongoing descending terms of A157904. Take the 
               dot product and add to the next term of A000055. a(4) = 17 = (1, 
               1, 1, 1) dot (1, 2, 4, 8) + 2 = 15 + 2.
%p A157904 with (numtheory): b:= proc(n) option remember; local d, j; if n<=1 then 
               n else (add (add (d*b(d), d= divisors(j)) *b(n-j), j=1..n-1))/ (n-1) 
               fi end: t:= proc(n) option remember; local k; `if` (n=0, 1, b(n)- 
               (add (b(k) *b(n-k), k=1..n-1) -`if` (type (n, odd), 0, b(n/2)))/2) 
               end: a:= proc(n) option remember; local i; if n<=0 then 1 else add 
               (t(i)*a(n-i-1),i=0..n) fi end: seq (a(n), n=0..35); [From Alois P. 
               Heinz (heinz(AT)hs-heilbronn.de), Mar 31 2009]
%Y A157904 Cf. A000055, A157905
%Y A157904 Sequence in context: A008999 A052903 A063457 this_sequence A002845 A072925 
               A002955
%Y A157904 Adjacent sequences: A157901 A157902 A157903 this_sequence A157905 A157906 
               A157907
%K A157904 nonn
%O A157904 0,2
%A A157904 Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 08 2009
%E A157904 More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Mar 31 2009