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05A10 - Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions

${n\choose r}$ is an integer owned by matte alternating factorial owned by PrimeFan an algebraic identity leading to Wilson's theorem owned by GeraW approximating the birthday problem owned by Algeboy asymptotics of central binomial coefficient owned by rspuzio binomial coefficient owned by matte birthday problem owned by PrimeFan Catalan numbers owned by bbukh central binomial coefficient owned by rspuzio combinations with repeated elements owned by kfgauss70 derivation of generating function for the reciprocal central binomial coefficients owned by rm50 divisibility of central binomial coefficient owned by rspuzio divisibility of prime-power binomial coefficients owned by rm50 double factorial owned by drini exponential factorial owned by CompositeFan factorial owned by yark factorial prime owned by PrimeFan factorion owned by CompositeFan falling factorial owned by rmilson Gaussian polynomials owned by mathcam generalized binomial coefficients owned by pahio generalized factorial owned by gilbert_51126 generalized Ruiz's identity owned by GeraW generating function for the reciprocal alternating central binomial coefficients owned by juanman generating function for the reciprocal central binomial coefficients owned by juanman generating function for the Catalan numbers owned by rm50 generating function for the reciprocal Catalan numbers owned by juanman Hosoya's triangle owned by PrimeFan inductive proof of binomial theorem owned by Mathprof Leibniz harmonic triangle owned by PrimeFan Levi-Civita permutation symbol owned by matte multinomial theorem owned by bshanks multinomial theorem (proof) owned by Koro Pascal's rule (bit string proof) owned by vampyr Pascal's rule proof owned by akrowne Pascal's triangle owned by Koro proof of generalized Ruiz's identity owned by GeraW proof of upper and lower bounds to binomial coefficient owned by rspuzio recursive algorithm for factorial function owned by PrimeFan Singmaster's conjecture owned by PrimeFan some formulas involving rising factorial owned by Wkbj79 sum of powers of binomial coefficients owned by Andrea Ambrosio Taylor series of arcus sine owned by pahio things counted by the Catalan numbers owned by rm50 upper and lower bounds to binomial coefficient owned by rspuzio
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