sum_(n=0)^∞ (B_n t^n)/(n!) = t/(exp(t) - 1)

B_n is a sequence with rational number values.

n | B_n | approximation 0 | 1 | 1 1 | -1/2 | -0.5 2 | 1/6 | 0.166667 3 | 0 | 0 4 | -1/30 | -0.0333333 5 | 0 | 0 6 | 1/42 | 0.0238095 7 | 0 | 0 8 | -1/30 | -0.0333333 9 | 0 | 0 10 | 5/66 | 0.0757576

B_n = ζ(1 - n) (-1) n for (n element Z and n>1)

B_n = B_n(0) for (n element Z and n>=0)

B_n = B_n(1) for (n element Z and n>1)

B_n = ( sum_(k=1)^n sum_(j=1)^k ((-1)^j j^n binomial(1 + n, -j + k))/binomial(n, k))/(1 + n) for (n element Z and n>0)

B_n = sum_(k=0)^n ((-1)^k k! S_n^(k))/(1 + k) for (n element Z and n>=0)

B_n = sum_(k=0)^n ( sum_(j=0)^k (-1)^j j^n binomial(k, j))/(1 + k) for (n element Z and n>0)

B_n = -2 i^n n integral_0^∞ t^(-1 + n)/(-1 + e^(2 π t)) dt for (n/2 element Z and n>0)

B_n = -i^n π integral_0^∞ t^n csch^2(π t) dt for (n/2 element Z and n>0)

B_n = 2^(1 - n) (-1 + n) n (i/π)^n integral_0^1 (log(1 - t) log^(-2 + n)(t))/t dt for (n/2 element Z and n>0)