binomialn

Binomialn is not a standard mathematical term. In most published sources, the string binomialn is either a misspelling of binomial, a variable name, or a label for a software function or project. There is no widely accepted definition, so its meaning must be inferred from context.

In mathematics, the closest established concepts are binomial and binomial coefficients. The binomial theorem states that for any nonnegative integer n, (x + y)^n = sum_{k=0}^n C(n, k) x^{n-k} y^k, where C(n, k) = n!/(k!(n−k)!) are the binomial coefficients. For real or complex n, a generalized binomial coefficient can be defined by C(n, k) = n(n−1)...(n−k+1)/k!, extending the expansion via the generalized binomial theorem.

In probability, the term binomial often refers to the binomial distribution, describing the number of successes in n independent Bernoulli trials with success probability p.

If binomialn appears in code, it is typically a variable or function name whose purpose is defined by the program. It may represent a binomial-like function, a numeric sequence, or a label for a computed result.

See also: binomial coefficient, binomial theorem, generalized binomial theorem, multinomial theorem, binomial distribution.