This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159062 #10 Jan 23 2019 10:53:16 %S A159062 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,16,17,18,19,20,21,22,22,23,24, %T A159062 25,26,27,27,28,29,30,31,32,32,33,34,35,36,37,37,38,39,40,41,41,42,43, %U A159062 44,45,45,46,47,48,49,49,50,51,52,53,53,54,55,56,57,57,58,59,60,61,61,62 %N A159062 Nearest integer to the variance of the number of tosses of a fair coin required to obtain at least n heads and n tails. %C A159062 For any n, either a(n+1)-a(n)=0 or a(n+1)-a(n)=1. %C A159062 a(n)/b(n) tends to 1 - 2/Pi as n tends to infinity, where b(n) is the n-th term of A159061. %D A159062 M. Griffiths, The Backbone of Pascal's Triangle, United Kingdom Mathematics Trust, 2008, pp. 68-72. %H A159062 M. Griffiths, <a href="https://www.jstor.org/stable/3621443">How many children?</a>, Math. Gaz., 90 (2006), 146-149. %F A159062 a(n) is the nearest integer to 2*n*(1+binomial(2*n,n)/(2^(2*n)))-((n*binomial(2*n,n))/(2^(2*n-1)))^2. %t A159062 f[n_] := Round[2^(1 - 4 n) n (16^n + Binomial[2 n, n] (4^n - 2 n Binomial[2 n, n]))]; Array[f, 72] %o A159062 (PARI) a(n) = round(2*n*(1+binomial(2*n,n)/(2^(2*n)))-((n*binomial(2*n,n))/(2^(2*n-1)))^2) \\ _Felix Fröhlich_, Jan 23 2019 %Y A159062 The nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails is given in A159061. %K A159062 easy,nonn %O A159062 1,1 %A A159062 _Martin Griffiths_, Apr 04 2009 %E A159062 More terms from _Robert G. Wilson v_, Apr 05 2009 %E A159062 Formula clarified by the author, Apr 06 2009