polinomis de suma de potencies

B_{0}(x) = x+(-1)(1/2)
B_{1}(x) = (1/2)x^{2}+(-1)(1/2)x+(1/12)
B_{2}(x) = (1/6)x^{3}+(-1)(1/4)x^{2}+(1/12)x
B_{3}(x) = (1/24)x^{4}+(-1)(1/12)x^{3}+(1/24)x^{2}+(-1)(1/720)
B_{4}(x) = (1/120)x^{5}+(-1)(1/48)x^{4}+(1/72)x^{3}+(-1)(1/720)x
B_{5}(x) = (1/720)x^{6}+(-1)(1/240)x^{5}+(1/288)x^{4}+(-1)(1/1440)x^{2}+...
...+(1/30240)
B_{6}(x) = (1/5040)x^{7}+(-1)(1/1440)x^{6}+(1/1440)x^{5}+(-1)(1/4320)x^{3}+...
...+(1/30240)x
B_{7}(x) = (1/40320)x^{8}+(-1)(1/10080)x^{7}+(1/8640)x^{6}+(-1)(1/17280)x^{4}+...
...+(1/60480)x^{2}+(-1)(1/1209600)
B_{8}(x) = (1/362880)x^{9}+(-1)(1/80640)x^{8}+(1/60480)x^{7}+(-1)(1/86400)x^{5}+...
...+(1/181440)x^{3}+(-1)(1/1209600)x
B_{9}(x) = (1/3628800)x^{10}+(-1)(1/725760)x^{9}+(1/483840)x^{8}+(-1)(1/518400)x^{6}+...
...+(1/725760)x^{4}+(-1)(1/2419200)x^{2}+(1/47900160)
B_{10}(x) = (1/39916800)x^{11}+(-1)(1/7257600)x^{10}+(1/4354560)x^{9}+(-1)(1/3628800)x^{7}+...
...+(1/3628800)x^{5}+(-1)(1/7257600)x^{3}+(1/47900160)x+B_{10}(0)


B_{n+1}(1) = B_{n+1}(0)
d_{x}[B_{n+1}(x)] = B_{n}(x)


1^{m}+...+n^{m} = m!( B_{m}(n+1)+(-1)B_{m}(1) )