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

1, 2, 6, 15, 41, 106, 284, 750, 2010, 5382, 14523, 39290, 106854, 291552, 798675, 2194828, 6051153, 16730373, 46383002, 128910484, 359115067, 1002575810, 2804667061, 7860780578, 22070885735, 62071872704, 174842835886, 493217417610

Offset: 0

Author

N. J. A. Sloane, Jan 20 2017

Keywords

• nonn

Links

• R. J. Mathar, Topologically Distinct Sets of Non-intersecting Circles in the Plane, arXiv:1603.00077 [math.CO], 2016. See (71).

Crossrefs

Cf. A269800, A280786, A280787, A027852.

Programs

Maple

A280788 := proc(N::integer)
    if N = 0 then
        1;
    else
        add(A000081(Nprime+1)*A027852(N-Nprime+2),Nprime=0..N) ;
    end if;
end proc:
seq(A280788(n),n=0..30) ; # R. J. Mathar, Mar 06 2017

Mathematica

a81[n_] := a81[n] = If[n <= 1, n, Sum[a81[n - j]*DivisorSum[j, #*a81[#]&], {j, n - 1}]/(n - 1)];
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];
A280788[n_] := If[n == 0, 1, Sum[a81[np+1]*A027852[n-np+2], {np, 0, n}]];
Table[A280788[n], {n, 0, 27}] (* Jean-François Alcover, Nov 23 2017, from Maple *)