kill(all)$

vector(input_expression):=
    block
    (
        define(u(x,k),input_expression),
        L:create_list(u(x,k),k,1,5),
        L:append(L,[u(x,n-1)]),
        L:append(L,[u(x,n)])
    )$

van = facebook.com/LearningCalculus$

q(k):=(k!)^2/(2*k!)$

f(x,k):=q(k) * x^k;
g(x,k):=k!/2 * x^k;

sum(f(x,k),k,1,inf);

vector(f(x,k));
vector(g(x,k));

a: vector(x^k);

b: vector(k!/2);

vector(x^k).vector(k!/2);

van=facebook.com/LearningCalculus$

G(x,k):=x^k*gamma(k+1);

2*sum(g(x,k),k,0,inf);
2*sum(G(x,k),k,0,inf);
2*vector(x^k).vector(k!/2);