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

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..406

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

Example

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

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

Mathematica

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

Crossrefs

Cf. A143968 (denominators), A001515.

Cf. A381845.

Sequence in context: A139891 A082113 A196597 * A243893 A012885 A162541

Adjacent sequences: A143988 A143989 A143990 * A143992 A143993 A143994

Keyword

nonn,frac,changed

Author

N. J. A. Sloane, Dec 02 2008

Status

approved