Divisibility of sum of multinomialsInteger-valued factorial ratiosPerron number distributionDesign constraint systems over the realsOn “The Average Height of Planted Plane Trees” by Knuth, de Bruijn and Rice (1972)Montgomery's conjecture and lower bound on certain Fourier transform.Distribution of the evaluation (at a non-trivial root of -1) of polynomials with small coefficientsCombinatorialProbabilistic Proof of Stirling's ApproximationGeneralizing Kasteleyn's formula even more?Derive a theoretical bound about coding with a partial eavesdropperTartaglia distribution
Divisibility of sum of multinomials Integer-valued factorial ratiosPerron number distributionDesign constraint systems over the realsOn “The Average Height of Planted Plane Trees” by Knuth, de Bruijn and Rice (1972)Montgomery's conjecture and lower bound on certain Fourier transform.Distribution of the evaluation (at a non-trivial root of -1) of polynomials with small coefficientsCombinatorialProbabilistic Proof of Stirling's ApproximationGeneralizing Kasteleyn's formula even more?Derive a theoretical bound about coding with a partial eavesdropperTartaglia distribution 6 3 $begingroup$ Let $n, m$ and $t$ be positive integers. Define the multi-family of sequences $$S(n,m,t)=sum_k_1+cdots+k_n=mbinommk_1,dots,k_n^t$$ where the sum runs over non-negative integers $k_1,dots,k_n$ . These numbers are related to average distances (from the origin) of uniform unit-step random walks on the plane. QUESTION. Is it always true that $n$ divides $S(n,m,t)$ ? Observe t
