A275208 Expansion of (A(x)^2-A(x^2))/2 where A(x) = A001006(x).

0, 1, 2, 6, 14, 38, 96, 256, 672, 1805, 4846, 13162, 35874, 98469, 271384, 751656, 2089640, 5831451, 16325950, 45847770, 129106738, 364498596, 1031480792, 2925337352, 8313200232, 23668977163, 67507731786, 192859753310, 551821286374, 1581188102590

Offset: 0

Author

R. J. Mathar, Jul 19 2016

Keywords

• nonn

Comments

Analog of A275166 with Motzkin numbers replacing connected graph counts.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A275207, A026940.

Programs

Maple

b:= proc(n) option remember; `if`(n<2, 1,
      ((3*(n-1))*b(n-2)+(1+2*n)*b(n-1))/(n+2))
    end:
a:= proc(n) option remember; add(b(j)*b(n-j), j=0..n/2)-
      `if`(n::odd, 0, (t-> t*(t+1)/2)(b(n/2)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Jul 19 2016

Mathematica

b[n_] := b[n] = If[n<2, 1, ((3*(n-1))*b[n-2] + (1+2*n)*b[n-1])/(n+2)];
a[n_] := a[n] = Sum[b[j]*b[n-j], {j, 0, n/2}] - If[OddQ[n], 0, Function[t, t*(t + 1)/2][b[n/2]]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 16 2017, after Alois P. Heinz *)

Formula

a(2n+1) = A275207(2n+1).