Feller, W. An introduction to probability theory and its applications. I. Third edition. (English) Zbl 0155.23101 New York-London-Sydney: John Wiley and Sons, Inc. XVIII, 509 p. (1968). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 20 ReviewsCited in 2243 Documents Keywords:probability theory PDF BibTeX XML OpenURL Online Encyclopedia of Integer Sequences: Pascal’s triangle read by rows: C(n,k) = binomial(n,k) = n!/(k!*(n-k)!), 0 <= k <= n. a(n) = 2^n - Fibonacci(n+2). Catalan’s triangle T(n,k) (read by rows): each term is the sum of the entries above and to the left, i.e., T(n,k) = Sum_{j=0..k} T(n-1,j). Triangle of number of n-tosses having a run of r or more heads for a fair coin with r=1 to n across and n=1, 2, ... down. a(n) is the number of n-tosses having a run of 3 or more heads for a fair coin (i.e., probability is a(n)/2^n). a(n) is the number of n-tosses having a run of 4 or more heads for a fair coin (i.e., probability is a(n)/2^n). a(n) is the number of n-tosses having a run of 5 or more heads for a fair coin (i.e., probability is a(n)/2^n). Decimal expansion of sqrt(2*log(2)). Number of 1D random walks with 8 steps where the median of the positions is n. a(n) = 64^n * Sum_{k=0..n} binomial(2*k,k)^3 / 64^k.