Series

Series(expr, {x, x0, n})

create a power series of expr up to order (x- x0)^n at the point x = x0

See:

>> Series(f(x),{x,a,3})
f(a)+f'(a)*(-a+x)+1/2*f''(a)*(-a+x)^2+1/6*Derivative(3)[f][a]*(-a+x)^3+O(-a+x)^4

>> nn=10; t=Rest(CoefficientList(Series(Product((1+x^(k*(k+1)/2)), {k, nn}), {x, 0, nn*(nn+1)/2}), x)); Flatten(Position(t, 0))
{2,5,8,12,23,33}