A038046 - OEIS

%I #20 May 09 2019 15:34:40

%S 1,1,3,6,12,17,32,39,63,81,120,131,213,226,311,377,503,520,742,761,

%T 1031,1169,1442,1465,2008,2093,2558,2801,3465,3494,4591,4622,5628,

%U 6054,7111,7390,9321,9358,10899,11616,13873,13914,17070,17113,20063,21509,24462

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

%C Eigensequence of triangle A126988. (i.e. the sequence shifts upon multiplication from the left by triangle A126988). - _Gary W. Adamson_, Apr 27 2009

%C Number of planted achiral trees with a distinguished leaf. - _Gus Wiseman_, Jul 31 2018

%H Alois P. Heinz, <a href="/A038046/b038046.txt">Table of n, a(n) for n = 1..10000</a>

%F a(1) = 1; a(n > 1) = Sum_{d|(n-1)} d * a((n-1)/d). - _Gus Wiseman_, Jul 31 2018

%F G.f. A(x) satisfies: A(x) = x * (1 + Sum_{j>=1} j*A(x^j)). - _Ilya Gutkovskiy_, May 09 2019

%e From _Gus Wiseman_, Jul 31 2018: (Start)

%e The a(5) = 12 planted achiral trees with a distinguished leaf:

%e   (Oooo), (oOoo), (ooOo), (oooO),

%e   ((O)(o)), ((o)(O)),

%e   ((Ooo)), ((oOo)), ((ooO)),

%e   (((Oo))), (((oO))),

%e   ((((O)))).

%e (End)

%p a:= proc(n) option remember; `if`(n<2, n, (m-> m*

%p       add(a(d)/d, d=numtheory[divisors](m)))(n-1))

%p     end:

%p seq(a(n), n=1..50);  # _Alois P. Heinz_, May 09 2019

%t a[n_]:=If[n==1,1,Sum[d*a[(n-1)/d],{d,Divisors[n-1]}]];

%t Array[a,30] (* _Gus Wiseman_, Jul 31 2018 *)

%Y Cf. A126988. - _Gary W. Adamson_, Apr 27 2009

%Y Cf. A000081, A002033, A003238, A004111, A007554, A038046, A067824, A317580.

%K nonn,eigen

%O 1,3

%A _Christian G. Bower_