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A275208 Expansion of (A(x)^2-A(x^2))/2 where A(x) = A001006(x). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Analog of A275166 with Motzkin numbers replacing connected graph counts.

LINKS

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

FORMULA

a(2n+1) = A275207(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=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-Fran├žois Alcover, May 16 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A275207, A026940.

Sequence in context: A122112 A190788 A168259 * A000634 A006654 A127546

Adjacent sequences:  A275205 A275206 A275207 * A275209 A275210 A275211

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jul 19 2016

STATUS

approved

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Last modified February 28 06:33 EST 2021. Contains 341695 sequences. (Running on oeis4.)