OFFSET
0,2
FORMULA
a(n) = [x^n] 1/((1-x)^(n+1)*(1-2*x-x^2+x^3)).
a(n) = Sum_{k=0..n} Sum_{i=0..k} binomial(k,i)*binomial(2*n+k-2*i+2, n-k)*(-1)^i.
G.f.: (2 - 7*x - 4*x^2 + x*sqrt(1-4*x))/(2 - 14*x + 16*x^2 + 30*x^3 + 8*x^4).
Conjecture: (-n+1)*a(n) + (7*n-9)*a(n-1) + 2*(-4*n+7)*a(n-2) + (-15*n+23)*a(n-3) + 2*(-2*n+3)*a(n-4) = 0. - R. J. Mathar, Jun 14 2016
MATHEMATICA
Table[Sum[Binomial[k, i]Binomial[2n+k-2i+2, n-k](-1)^i, {k, 0, n}, {i, 0, k}], {n, 0, 12}]
PROG
(Maxima) makelist(sum(sum(binomial(k, i)*binomial(2*n+k-2*i+2, n-k)*(-1)^i, i, 0, k), k, 0, n), n, 0, 12);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Apr 01 2011
STATUS
approved