The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A301280 Nearest integer to variance of n-th row of Pascal's triangle. 4
 0, 0, 0, 1, 5, 16, 56, 198, 699, 2490, 8943, 32355, 117800, 431316, 1587207, 5867244, 21777203, 81127591, 303240041, 1136914129, 4274441613, 16111746161, 60873695892, 230495640009, 874525192278, 3324270554675, 12658405644200, 48280298159610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Robert Israel, Table of n, a(n) for n = 0..1667 Simon Demers, Taylor's Law Holds for Finite OEIS Integer Sequences and Binomial Coefficients, American Statistician, Volume 72, 2018 - Issue 4. FORMULA From Robert Israel, Jul 18 2019: (Start) The variance is binomial(2*n,n)/n - 4^n/(n*(n+1)). a(n) ~ 4^n/((sqrt(Pi)*n^(3/2)). (End) EXAMPLE The first few variances are 0, 0, 1/3, 4/3, 47/10, 244/15, 1186/21, 1384/7, 25147/36, 112028/45, 98374/11, 1067720/33, 1531401/13, 39249768/91, 166656772/105, 88008656/15, 2961699667/136, 12412521388/153, 51854046982/171, 108006842264/95, 448816369361/105, ... MAPLE M:=70; m := n -> 2^n/(n+1); m1:=[seq(m(n), n=0..M)]; # A084623/A000265 v := n -> (1/n) * add((binomial(n, i) - m(n))^2, i=0..n ); v1:= [0, 0, seq(v(n), n=2..60)]; # A301278/A301279 and A301280 # Alternative: f:= n -> round((binomial(2*n, n)-4^n/(n+1))/n): f(0):=0: map(f, [\$0..60]); # Robert Israel, Jul 18 2019 CROSSREFS Mean and variance of n-th row of Pascal's triangle: A084623/A000265, A301278/A301279, A054650. Sequence in context: A299685 A268225 A120343 * A153366 A057553 A226973 Adjacent sequences: A301277 A301278 A301279 * A301281 A301282 A301283 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 18 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 26 00:10 EDT 2023. Contains 365649 sequences. (Running on oeis4.)