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INVERT transform of A055615, n*mu(n).
2

%I #13 May 18 2018 08:41:37

%S 1,1,-1,-6,-7,3,36,55,-9,-221,-373,-18,1290,2506,643,-7488,-16487,

%T -7258,42577,106701,65695,-236923,-681856,-534130,1282512,4304675,

%U 4079414,-6687222,-26866199,-29871373,33019148,165771711,212092381,-149113958,-1010995614

%N INVERT transform of A055615, n*mu(n).

%C Equals row sums of triangle A144029.

%H Alois P. Heinz, <a href="/A144028/b144028.txt">Table of n, a(n) for n = 0..2000</a>

%F a(4) = -7 = (0, -3, -2, 1) dot (1, 1, -1, -6); where (0, -3, -2, 1) = the first 4 terms of n*mu(n) reversed. (1, 1, -1, -6) = the first 4 terms of the INVERT recursion operation.

%p a:= proc(n) option remember; `if`(n=0, 1,

%p add(a(n-i)*i*numtheory[mobius](i), i=1..n))

%p end:

%p seq(a(n), n=0..40); # _Alois P. Heinz_, Sep 22 2017

%t a[n_] := a[n] = If[n == 0, 1, Sum[a[n-i]*i*MoebiusMu[i], {i, 1, n}]];

%t Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, May 18 2018, translated from Maple *)

%Y Cf. A055615, A144029.

%K sign

%O 0,4

%A _Gary W. Adamson_, Sep 07 2008

%E Corrected from a(9) onwards by _R. J. Mathar_, Jan 27 2011

%E a(0)=1 prepended by _Alois P. Heinz_, Sep 22 2017