Kirschenhofer, Peter et Prodinger, Helmut, The higher moments of the number of returns of a simple random walk, Advances in applied probability , 26(2), 1994, pp. 561-563
We consider a simple random walk starting at 0 and leading to 0 after 2n steps. By a generating functions approach we achieve closed formulae for the moments of the random variables .number of visits to the origin'.