OFFSET
0,1
COMMENTS
Note: the term in x^11 in the series expansion above has a common factor of 7 between the numerator and denominator and is usually written 34807/364953600. The common factor of 7 occurs at n=6, 9, 12, etc. The sequence of the coefficients can be generated by combining this series with A002067.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..210
FORMULA
a(n) = (2*n+1)!*2^(n+1).
From Amiram Eldar, Jan 14 2021: (Start)
Sum_{n>=0} 1/a(n) = sinh(1/sqrt(2))/sqrt(2).
Sum_{n>=0} (-1)^n/a(n) = sin(1/sqrt(2))/sqrt(2). (End)
EXAMPLE
InverseErf(x) = (1/2*sqrt(Pi))*x + (1/24*Pi^(3/2))*x^3 + (7/960*Pi^(5/2))*x^5 + (127/80640*Pi^(7/2))*x^7 + (4369/11612160*Pi^(9/2))*x^9 + (243649/2554675200*Pi^(11/2))*x^11 + ...
MAPLE
denominators:=[seq((2*n+1)!*2^(n+1), n=0..14)]; a:=proc(n) if(n < 2) then RETURN(1) fi; sum('binomial(2*n, 2*k)*a(k)*a(n-k-1)', 'k'=0..n-1); end; numerators:=[seq(a(n), n=0..14)];
MATHEMATICA
Table[(2*n + 1)!*2^(n + 1), {n, 0, 25}] (* G. C. Greubel, Mar 19 2017 *)
PROG
(PARI) for(n=0, 25, print1((2*n+1)!*2^(n+1), ", ")) \\ G. C. Greubel, Mar 19 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Marcus Blackburn (marcus.blackburn(AT)dial.pipex.com), Sep 20 2006
STATUS
approved