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

Author

Emanuele Munarini, Apr 06 2012

Keywords

• nonn

Programs

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}]

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);

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).