Polynomials b_n(x) which form a Sheffer sequence with g(t) | = | t/(e^t - 1) f(t) | = | e^t - 1, giving generating function sum_(k = 0)^∞ (b_k(x))/(k!) t^k = (t(t + 1)^x)/(ln(1 + t)). Roman defines Bernoulli numbers of the second kind as b_n = b_n(0). They are related to the Stirling numbers of the first kind s(n, m) by b_n(x) = b_n(0) + sum_(k = 1)^n n/k s(n - 1, k - 1) x^k (Roman 1984, p.

Bernoulli number of the second kind | Bernoulli polynomial | Sheffer sequence | Stirling number of the first kind

Jacob Bernoulli