A092676 Numerators of coefficients in the series for inverf(2x/sqrt(Pi)).

1, 1, 7, 127, 4369, 34807, 20036983, 2280356863, 49020204823, 65967241200001, 15773461423793767, 655889589032992201, 94020690191035873697, 655782249799531714375489, 44737200694996264619809969

Offset

1,3

Comments

Differs from A002067(n) at n = 6, 9, 12, ....

Following Blair et al., we use the notation inverf() for the inverse of the error function.

Links

G. C. Greubel, Table of n, a(n) for n = 1..230

G. Alkauskas, Algebraic and abelian solutions to the projective translation equation, arXiv preprint arXiv:1506.08028 [math.AG], 2015-2016; Aequationes Math. 90 (4) (2016), 727-763.

J. M. Blair, C. A. Edwards and J. H. Johnson, Rational Chebyshev approximations for the inverse of the error function, Math. Comp. 30 (1976), 827-830.

L. Carlitz, The inverse of the error function, Pacific J. Math., 13 (1963), 459-470.

Eric Weisstein, Mathematica program and first 50 terms of the series

Eric Weisstein's World of Mathematics, Inverse Erf

Wikipedia, Error Function

Example

Inverf(2x/sqrt(Pi)) = x + x^3/3 + 7x^5/30 + 127x^7/630 + 4369x^9/22680 + 34807x^11/178200 + ...
The first few coefficients are 1, 1, 7/6, 127/90, 4369/2520, 34807/16200, 20036983/7484400, 2280356863/681080400, ...

Maple

c:=proc(n) option remember; if n <= 0 then 1 else add( c(k)*c(n-k-1)/((k+1)*(2*k+1)), k=0..n-1 ) fi; end;

Mathematica

Numerator[CoefficientList[Series[InverseErf[2*x/Sqrt[Pi]], {x, 0, 50}], x]][[2 ;; ;; 2]] (* G. C. Greubel, Jan 09 2017 *)

Crossrefs

Cf. A002067, A092677, A052712. For denominators see A132467.

Sequence in context: A274673 A363870 A215066 * A002067 A274571 A336502

Adjacent sequences: A092673 A092674 A092675 * A092677 A092678 A092679

Keyword

nonn,frac

Author

Eric W. Weisstein, Mar 02 2004

Extensions

Edited by N. J. A. Sloane, Nov 15 2007

Status

approved