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A007463 Shifts left under lcm-convolution with itself.

%I A007463 M1457 #26 Oct 07 2017 00:08:31
%S A007463 1,1,2,5,14,40,128,369,1214,3516,12776,40534,137404,463232,1602348,
%T A007463 5216253,17753898,58597316,212150928,710453534,2366853608,8584498376,
%U A007463 30026959300,100396304016,333997297900,1157269900344,3852364562536,13917848281928,45618032373712
%N A007463 Shifts left under lcm-convolution with itself.
%D A007463 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007463 Alois P. Heinz, <a href="/A007463/b007463.txt">Table of n, a(n) for n = 0..550</a>
%H A007463 M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
%H A007463 M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
%p A007463 a:= proc(n) option remember;
%p A007463       `if`(n=0, 1, add(ilcm(a(i), a(n-1-i)), i=0..n-1))
%p A007463     end:
%p A007463 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jun 22 2012
%t A007463 a[0]=1; a[1]=1; a[n_] := a[n] = Sum[LCM[a[k], a[n-k-1]], {k, 0, n-1}]; Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Sep 07 2012, after _Alois P. Heinz_ *)
%o A007463 (PARI) N=66; v=vector(N);  v[1]=1; for(n=2,N, v[n]=sum(k=1,n-1, lcm(v[k],v[n-k])) ); v  \\ _Joerg Arndt_, Jun 30 2013
%K A007463 nonn,nice,eigen
%O A007463 0,3
%A A007463 _N. J. A. Sloane_