cp's OEIS Frontend

A280788 Convolution of A000081 and A027852, shifted by 3 leading zeros.

%I A280788 #20 Nov 23 2017 03:01:20
%S A280788 1,2,6,15,41,106,284,750,2010,5382,14523,39290,106854,291552,798675,
%T A280788 2194828,6051153,16730373,46383002,128910484,359115067,1002575810,
%U A280788 2804667061,7860780578,22070885735,62071872704,174842835886,493217417610
%N A280788 Convolution of A000081 and A027852, shifted by 3 leading zeros.
%H A280788 R. J. Mathar, <a href="http://arxiv.org/abs/1603.00077">Topologically Distinct Sets of Non-intersecting Circles in the Plane</a>, arXiv:1603.00077 [math.CO], 2016. See (71).
%p A280788 A280788 := proc(N::integer)
%p A280788     if N = 0 then
%p A280788         1;
%p A280788     else
%p A280788         add(A000081(Nprime+1)*A027852(N-Nprime+2),Nprime=0..N) ;
%p A280788     end if;
%p A280788 end proc:
%p A280788 seq(A280788(n),n=0..30) ; # _R. J. Mathar_, Mar 06 2017
%t A280788 a81[n_] := a81[n] = If[n <= 1, n, Sum[a81[n - j]*DivisorSum[j, #*a81[#]&], {j, n - 1}]/(n - 1)];
%t A280788 A027852[n_] := Module[{dh = 0, np}, For[np = 0, np <= n, np++, dh = a81[np] * a81[n - np] + dh]; If[EvenQ[n], dh = a81[n/2] + dh]; dh/2];
%t A280788 A280788[n_] := If[n == 0, 1, Sum[a81[np+1]*A027852[n-np+2], {np, 0, n}]];
%t A280788 Table[A280788[n], {n, 0, 27}] (* _Jean-François Alcover_, Nov 23 2017, from Maple *)
%Y A280788 Cf. A269800, A280786, A280787, A027852.
%K A280788 nonn
%O A280788 0,2
%A A280788 _N. J. A. Sloane_, Jan 20 2017