{ "Title": "Bernoulli numbers", "Definition": "The Bernoulli numbers $B_n$ are the coefficients of the exponential generating function $\\frac{t}{e^t-1} = \\sum_{n=0}^\\infty \\frac{B_nt^n}{n!}$.", "Parameters": { "n": { "type": "Z", "constraints": "$n \\geq 0$" } }, "Comments": { "comment-sign-convention": "Some authors prefer to define $B^+_n = (-1)^n B_n$ as Bernoulli numbers.", "comment-polynomials": "$B_n = B_n(0)$, the constant term of the $n$-th HREF{Bernoulli_polynomials}[Bernoulli polynomial]. These polynomials express HREF{Sums_of_powers}[sums of powers]: $\\sum_{k