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Shifts left under Euler transform.
2

%I #21 Nov 08 2020 05:58:49

%S -1,-1,-1,0,1,2,0,-3,-5,-1,11,19,4,-42,-78,-18,172,333,88,-747,-1483,

%T -436,3355,6834,2193,-15417,-32248,-11206,72264,154900,57929,-344282,

%U -755103,-302126,1661464,3726663,1586904,-8103245,-18581402,-8384292,39876825

%N Shifts left under Euler transform.

%H Alois P. Heinz, <a href="/A038072/b038072.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%p with(numtheory): a:= proc(n) option remember; local d,j; if n=1 then -1 else (add(d*a(d), d=divisors(n-1)) +add(add(d*a(d), d=divisors(j)) *a(n-j), j=1..n-2))/(n-1) fi end: seq(a(n), n=1..40); # _Alois P. Heinz_, Sep 06 2008

%t a[n_] := a[n] = If[n == 1, -1, (Sum[d a[d], {d, Divisors[n-1]}] + Sum[Sum[d a[d], {d, Divisors[j]}] a[n-j], {j, 1, n-2}])/(n-1)];

%t Array[a, 40] (* _Jean-François Alcover_, Nov 08 2020, after _Alois P. Heinz_ *)

%Y Cf. A038073.

%K sign,eigen

%O 1,6

%A _Christian G. Bower_, Jan 04 1999