A275210 Expansion of (A(x)^2-A(x^2))/2 where A(x) = A001006(x)-1.

0, 0, 0, 2, 5, 17, 45, 129, 349, 970, 2658, 7364, 20363, 56634, 157750, 441084, 1236173, 3474672, 9789568, 27648486, 78254719, 221951037, 630717569, 1795576937, 5120472435, 14625574662, 41837913310, 119851980508, 343798008165, 987445317761, 2839518208661

Offset

0,4

Comments

Analog of A216785 with Motzkin numbers replacing connected graph counts.

Links

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

Formula

a(2n+1) = A275209(2n+1).

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=1..n/2)-
      `if`(n=0 or 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, 1, n/2}] - If[n == 0 || 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 *)

Crossrefs

Cf. A275209.

Sequence in context: A063106 A096295 A215580 * A219554 A074494 A051438

Adjacent sequences: A275207 A275208 A275209 * A275211 A275212 A275213

Keyword

nonn

Author

R. J. Mathar, Jul 19 2016

Status

approved