A182016 Central coefficients of triangle A182013.

1, 3, 15, 85, 531, 3545, 24833, 180251, 1344163, 10237001, 79287469, 622596063, 4945078477, 39658283943, 320689293119, 2611817435525, 21405148148051, 176396318594937, 1460795339822349, 12150467810552223, 101463416752305385, 850306144532133787

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = sum(M(i),i=n..2*n), where the M(n)'s are the Motzkin numbers.

Recurrence: a(n+1) = a(n) + M(2n+2) + M(2n+1) - M(n).

Mathematica

M[n_]:=If[n==0, 1, Coefficient[(1+x+x^2)^(n+1), x^n]/(n+1)]; Table[Sum[M[i], {i, n, 2n}], {n, 0, 40}]

Prog

(Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)), x^n)/(n+1);
makelist(sum(M(i), i, n, 2*n), n, 0, 20);

Crossrefs

Sequence in context: A118342 A084209 A317133 * A127085 A326275 A093615

Adjacent sequences: A182013 A182014 A182015 * A182017 A182018 A182019

Keyword

nonn

Author

Emanuele Munarini, Apr 06 2012

Status

approved