A fairly direct consequence of the indefinite sum m Sum Pochhammer(k,p) = Pochhammer(m,p+1)/(p+1), k=1 which is in turn a direct consequence of the rule of formation of Pascal's triangle, nCk + nC(k+1) = (n+1)C(k+1), is bern(p) = -(-1)^j*(p+j)*sum((-1)^k*stirling_s1(k+1,j)*stirling_s2(p+j-1,k)/(k+1),k,0,p+j-1)/binom(p+j,j) p + j - 1 k ==== (- 1) s S j \ k + 1, j p + j - 1, k (- 1) (p + j) > ------------------------------ / k + 1 ==== k = 0 B = - -------------------------------------------------------, p>0. p binom(p + j, j) For p:=1, bern(p) = sum((-1)^k*k!*stirling_s2(p,k)/(k+1),k,0,p) p k ==== (- 1) k! S \ p, k B = > ---------------. p / k + 1 ==== k = 0 This latter, at least, must be in G, Knuth, and P. --rwg