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A051573 INVERTi transform of A000081 = [1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12486,...].

%I A051573 #19 Mar 28 2015 11:50:00
%S A051573 1,1,1,2,3,8,16,41,98,250,631,1646,4285,11338,30135,80791,217673,
%T A051573 590010,1606188,4392219,12055393,33206321,91752211,254261363,
%U A051573 706465999,1967743066,5493195530,15367129299,43073007846,120949992543,340206026166,958444631917
%N A051573 INVERTi transform of A000081 = [1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12486,...].
%H A051573 Alois P. Heinz, <a href="/A051573/b051573.txt">Table of n, a(n) for n = 0..1000</a>
%H A051573 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A051573 a(n) ~ c * d^n / n^(3/2), where d = A051491 = 2.9557652856519949747148175241..., c = A187770 = 0.4399240125710253040409033914... . - _Vaclav Kotesovec_, Sep 06 2014
%p A051573 with(numtheory):
%p A051573 b:= proc(n) option remember; local d, j; `if` (n<2, n,
%p A051573       (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))
%p A051573     end:
%p A051573 a:= proc(n) option remember; local i; `if`(n<0, -1,
%p A051573       -add(a(n-i) *b(i+1), i=1..n+1))
%p A051573     end:
%p A051573 seq(a(n), n=0..40);  # _Alois P. Heinz_, May 17 2013
%t A051573 b[n_] := b[n] = If[n < 2, n, Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n-j], {j, 1, n-1}]/(n-1)]; a[n_] := a[n] = If[n < 0, -1, -Sum[a[n-i]*b[i+1], {i, 1, n+1}]]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Apr 16 2014, after _Alois P. Heinz_ *)
%Y A051573 Cf. A052250, A000081.
%K A051573 nonn
%O A051573 0,4
%A A051573 _N. J. A. Sloane_