A051550 - OEIS

%I #18 Jan 17 2025 03:36:14

%S 1,-1,7,-65,695,-8081,33101,-422987,5564765,-224617265,3076621127,

%T -42757939841,601443961207,-8546453367505,122502619954855,

%U -65523500154995,2857425741902815,-41776517795212585,1841741396312128685,-27188436143675219435

%N Numerators in expansion of 1/(10+sqrt(36+x)).

%C The program confirms that the "dip" in magnitude near a(15) is correct. - _R. J. Mathar_, Oct 31 2006

%D Bruce C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, 1991, see p. 92, Eq. 2.5.

%H Amiram Eldar, <a href="/A051550/b051550.txt">Table of n, a(n) for n = 0..350</a>

%e Fractions begin with 1/16, -1/3072, 7/1769472, -65/1019215872, 695/587068342272, -8081/338151365148672, 33101/64925062108545024, -422987/37396835774521933824, 5564765/21540577406124633882624, ...

%p A051550 := proc(n) s := taylor( 1/(10+sqrt(36+x)),x=0,n+1) ; coeftayl(s,x=0,n) ; end: for n from 0 to 30 do printf("%a,",numer(A051550(n))) ; end: # _R. J. Mathar_, Oct 31 2006

%t CoefficientList[Series[1/(10+Sqrt[36+x]),{x,0,20}],x]//Numerator (* _Harvey P. Dale_, Dec 16 2020 *)

%Y Cf. A051551 (denominators).

%K sign,frac

%O 0,3

%A _N. J. A. Sloane_