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Numerators of numbers with g.f. exp(1-(1-x)^(1/2)).
4

%I #12 Nov 23 2024 12:47:08

%S 1,1,1,7,37,133,2431,27007,176761,5329837,12994393,866792053,

%T 5213746711,841146804577,10532583170701,569600638022431,

%U 16539483668991901,3333075288160853,16955228098102446847,932411737877492011,10996483739066355827053,66024590609554132070857

%N Numerators of numbers with g.f. exp(1-(1-x)^(1/2)).

%H Robert Israel, <a href="/A143991/b143991.txt">Table of n, a(n) for n = 0..406</a>

%e 1, 1/2, 1/4, 7/48, 37/384, 133/1920, 2431/46080, 27007/645120, 176761/5160960, ...

%p S:= series(exp(1-(1-x)^(1/2)),x,21):

%p seq(numer(coeff(S,x,i)),i=0..20); # _Robert Israel_, Mar 23 2023

%t CoefficientList[Series[Exp[1-Sqrt[1-x]],{x,0,30}],x]//Numerator (* _Harvey P. Dale_, Nov 23 2024 *)

%Y Cf. A143968 (denominators), A001515.

%K nonn,frac,changed

%O 0,4

%A _N. J. A. Sloane_, Dec 02 2008