A143991 Numerators of numbers with g.f. exp(1-(1-x)^(1/2)).
1, 1, 1, 7, 37, 133, 2431, 27007, 176761, 5329837, 12994393, 866792053, 5213746711, 841146804577, 10532583170701, 569600638022431, 16539483668991901, 3333075288160853, 16955228098102446847, 932411737877492011, 10996483739066355827053, 66024590609554132070857
Offset: 0
Examples
1, 1/2, 1/4, 7/48, 37/384, 133/1920, 2431/46080, 27007/645120, 176761/5160960, ...
Links
- Robert Israel, Table of n, a(n) for n = 0..406
Programs
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Maple
S:= series(exp(1-(1-x)^(1/2)),x,21): seq(numer(coeff(S,x,i)),i=0..20); # Robert Israel, Mar 23 2023
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Mathematica
CoefficientList[Series[Exp[1-Sqrt[1-x]],{x,0,30}],x]//Numerator (* Harvey P. Dale, Nov 23 2024 *)
Formula
Conjecture: a(n) = numerator( (e/Pi)*Integral_{x=-oo..+oo} cos(x)/(1 + x^2)^n dx ) for n > 0. See A381845 for the numerators of this integral. - Stefano Spezia, Mar 12 2025