A122551 Denominators of the coefficients of the series for InverseErf(x).

2, 24, 960, 80640, 11612160, 2554675200, 797058662400, 334764638208000, 182111963185152000, 124564582818643968000, 104634249567660933120000, 105889860562472864317440000, 127067832674967437180928000000

Offset: 0

Author

Marcus Blackburn (marcus.blackburn(AT)dial.pipex.com), Sep 20 2006

Keywords

• easy
• nonn

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.

Examples

			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 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..210

Crossrefs

Cf. A002067, A092676.

Programs

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 *)

PARI

for(n=0,25, print1((2*n+1)!*2^(n+1), ", ")) \\ G. C. Greubel, Mar 19 2017

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)