cp's OEIS Frontend

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

%I A092676 #35 Feb 16 2025 08:32:52
%S A092676 1,1,7,127,4369,34807,20036983,2280356863,49020204823,65967241200001,
%T A092676 15773461423793767,655889589032992201,94020690191035873697,
%U A092676 655782249799531714375489,44737200694996264619809969
%N A092676 Numerators of coefficients in the series for inverf(2x/sqrt(Pi)).
%C A092676 Differs from A002067(n) at n = 6, 9, 12, ....
%C A092676 Following Blair et al., we use the notation inverf() for the inverse of the error function.
%H A092676 G. C. Greubel, <a href="/A092676/b092676.txt">Table of n, a(n) for n = 1..230</a>
%H A092676 G. Alkauskas, <a href="http://arxiv.org/abs/1506.08028">Algebraic and abelian solutions to the projective translation equation</a>, arXiv preprint arXiv:1506.08028 [math.AG], 2015-2016; Aequationes Math. 90 (4) (2016), 727-763.
%H A092676 J. M. Blair, C. A. Edwards and J. H. Johnson, <a href="https://doi.org/10.1090/S0025-5718-1976-0421040-7">Rational Chebyshev approximations for the inverse of the error function</a>, Math. Comp. 30 (1976), 827-830.
%H A092676 L. Carlitz, <a href="http://projecteuclid.org/euclid.pjm/1103035736">The inverse of the error function</a>, Pacific J. Math., 13 (1963), 459-470.
%H A092676 Eric Weisstein, <a href="/A092676/a092676.txt">Mathematica program and first 50 terms of the series</a>
%H A092676 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/InverseErf.html">Inverse Erf</a>
%H A092676 Wikipedia, <a href="http://en.wikipedia.org/wiki/Error_function">Error Function</a>
%e A092676 Inverf(2x/sqrt(Pi)) = x + x^3/3 + 7x^5/30 + 127x^7/630 + 4369x^9/22680 + 34807x^11/178200 + ...
%e A092676 The first few coefficients are 1, 1, 7/6, 127/90, 4369/2520, 34807/16200, 20036983/7484400, 2280356863/681080400, ...
%p A092676 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;
%t A092676 Numerator[CoefficientList[Series[InverseErf[2*x/Sqrt[Pi]], {x, 0, 50}], x]][[2 ;; ;; 2]] (* _G. C. Greubel_, Jan 09 2017 *)
%Y A092676 Cf. A002067, A092677, A052712. For denominators see A132467.
%K A092676 nonn,frac
%O A092676 1,3
%A A092676 _Eric W. Weisstein_, Mar 02 2004
%E A092676 Edited by _N. J. A. Sloane_, Nov 15 2007