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A038046 Shifts left under transform T where Ta is (identity) DCONV a.

%I A038046 #20 May 09 2019 15:34:40
%S A038046 1,1,3,6,12,17,32,39,63,81,120,131,213,226,311,377,503,520,742,761,
%T A038046 1031,1169,1442,1465,2008,2093,2558,2801,3465,3494,4591,4622,5628,
%U A038046 6054,7111,7390,9321,9358,10899,11616,13873,13914,17070,17113,20063,21509,24462
%N A038046 Shifts left under transform T where Ta is (identity) DCONV a.
%C A038046 Eigensequence of triangle A126988. (i.e. the sequence shifts upon multiplication from the left by triangle A126988). - _Gary W. Adamson_, Apr 27 2009
%C A038046 Number of planted achiral trees with a distinguished leaf. - _Gus Wiseman_, Jul 31 2018
%H A038046 Alois P. Heinz, <a href="/A038046/b038046.txt">Table of n, a(n) for n = 1..10000</a>
%F A038046 a(1) = 1; a(n > 1) = Sum_{d|(n-1)} d * a((n-1)/d). - _Gus Wiseman_, Jul 31 2018
%F A038046 G.f. A(x) satisfies: A(x) = x * (1 + Sum_{j>=1} j*A(x^j)). - _Ilya Gutkovskiy_, May 09 2019
%e A038046 From _Gus Wiseman_, Jul 31 2018: (Start)
%e A038046 The a(5) = 12 planted achiral trees with a distinguished leaf:
%e A038046   (Oooo), (oOoo), (ooOo), (oooO),
%e A038046   ((O)(o)), ((o)(O)),
%e A038046   ((Ooo)), ((oOo)), ((ooO)),
%e A038046   (((Oo))), (((oO))),
%e A038046   ((((O)))).
%e A038046 (End)
%p A038046 a:= proc(n) option remember; `if`(n<2, n, (m-> m*
%p A038046       add(a(d)/d, d=numtheory[divisors](m)))(n-1))
%p A038046     end:
%p A038046 seq(a(n), n=1..50);  # _Alois P. Heinz_, May 09 2019
%t A038046 a[n_]:=If[n==1,1,Sum[d*a[(n-1)/d],{d,Divisors[n-1]}]];
%t A038046 Array[a,30] (* _Gus Wiseman_, Jul 31 2018 *)
%Y A038046 Cf. A126988. - _Gary W. Adamson_, Apr 27 2009
%Y A038046 Cf. A000081, A002033, A003238, A004111, A007554, A038046, A067824, A317580.
%K A038046 nonn,eigen
%O A038046 1,3
%A A038046 _Christian G. Bower_