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%I #12 Jan 14 2021 04:43:37
%S 2,24,960,80640,11612160,2554675200,797058662400,334764638208000,
%T 182111963185152000,124564582818643968000,104634249567660933120000,
%U 105889860562472864317440000,127067832674967437180928000000
%N Denominators of the coefficients of the series for InverseErf(x).
%C 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.
%H G. C. Greubel, <a href="/A122551/b122551.txt">Table of n, a(n) for n = 0..210</a>
%F a(n) = (2*n+1)!*2^(n+1).
%F From _Amiram Eldar_, Jan 14 2021: (Start)
%F Sum_{n>=0} 1/a(n) = sinh(1/sqrt(2))/sqrt(2).
%F Sum_{n>=0} (-1)^n/a(n) = sin(1/sqrt(2))/sqrt(2). (End)
%e 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 + ...
%p 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)];
%t Table[(2*n + 1)!*2^(n + 1), {n,0,25}] (* _G. C. Greubel_, Mar 19 2017 *)
%o (PARI) for(n=0,25, print1((2*n+1)!*2^(n+1), ", ")) \\ _G. C. Greubel_, Mar 19 2017
%Y Cf. A002067, A092676.
%K easy,nonn
%O 0,1
%A Marcus Blackburn (marcus.blackburn(AT)dial.pipex.com), Sep 20 2006
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