A101683 Write exp(sqrt(1+x)-1) = Sum c(n) x^n/n!; then a(n) = numerator of c(n).

1, 1, 0, 1, -5, 9, -329, 3655, -11961, 721315, -12310199, 29326887, -4939227215, 113836841041, -356357531655, 77087063678521, -2238375706930349, 17366683494629835, -2294640596998068569, 80381887628910919255

Offset

0,5

Comments

Odd part of A000806.

Links

Robert Israel, Table of n, a(n) for n = 0..404

Formula

Numerator of c(n) satisfying c(n) = (c(n-2) - (4*n-6)*c(n-1))/4, c(0) = 1, c(1) = 1/2. - Robert Israel, Nov 30 2023

Example

exp(sqrt(1+x)-1) = 1+(1/2)*x+(1/48)*x^3-(5/384)*x^4+(3/320)*x^5-(329/46080)*x^6+(731/129024)*x^7-(1329/286720)*x^8+... - From N. J. A. Sloane, Aug 29 2012

Maple

c[0]:= 1: c[1]:= 1/2:
for n from 2 to 100 do c[n]:= (c[n-2]-(4*n-6)*c[n-1])/4 od:
seq(numer(c[n]), n=0..100); # Robert Israel, Nov 30 2023

Mathematica

With[{nn=20}, Numerator[CoefficientList[Series[Exp[Sqrt[1+x]-1], {x, 0, nn}], x]Range[0, nn]!]] (* Harvey P. Dale, Aug 29 2012 *)

Prog

(PARI) my(x='x+O('x^30)); apply(numerator, Vec(serlaplace(exp(sqrt(1+x)-1)))) \\ Michel Marcus, Nov 30 2023

Crossrefs

Denominators are 2^A101684(n).

Sequence in context: A046093 A097086 A109076 * A348132 A098135 A112259

Adjacent sequences: A101680 A101681 A101682 * A101684 A101685 A101686

Keyword

sign,frac

Author

Ralf Stephan, Dec 13 2004

Extensions

Definition clarified by N. J. A. Sloane, Aug 29 2012

Status

approved