BinomialSequence.cs

using System.Collections.Generic;
using System.Numerics;

namespace Algorithms.Sequences
{
    /// <summary>
    ///     <para>
    ///         Sequence of binomial coefficients.
    ///     </para>
    ///     <para>
    ///         Wikipedia: https://en.wikipedia.org/wiki/Binomial_coefficient.
    ///     </para>
    ///     <para>
    ///         OEIS: http://oeis.org/A007318.
    ///     </para>
    /// </summary>
    public class BinomialSequence : ISequence
    {
        /// <summary>
        ///     Gets sequence of binomial coefficients.
        /// </summary>
        public IEnumerable<BigInteger> Sequence
        {
            get
            {
                var i = 0;

                while (true)
                {
                    var row = GenerateRow(i);
                    foreach (var coefficient in row)
                    {
                        yield return coefficient;
                    }

                    i++;
                }
            }
        }

        private static BigInteger BinomialCoefficient(long n, long k)
        {
            if (k == 0 || k == n)
            {
                return new BigInteger(1);
            }

            if (n < 0)
            {
                return new BigInteger(0);
            }

            return BinomialCoefficient(n - 1, k) + BinomialCoefficient(n - 1, k - 1);
        }

        private static IEnumerable<BigInteger> GenerateRow(long n)
        {
            long k = 0;

            while (k <= n)
            {
                yield return BinomialCoefficient(n, k);
                k++;
            }
        }
    }
}