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A101683
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Write exp(sqrt(1+x)-1) = Sum c(n) x^n/n!; then a(n) = numerator of c(n).
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2
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1, 1, 0, 1, -5, 9, -329, 3655, -11961, 721315, -12310199, 29326887, -4939227215, 113836841041, -356357531655, 77087063678521, -2238375706930349, 17366683494629835, -2294640596998068569, 80381887628910919255
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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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
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EXAMPLE
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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
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MAPLE
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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:
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MATHEMATICA
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With[{nn=20}, Numerator[CoefficientList[Series[Exp[Sqrt[1+x]-1], {x, 0, nn}], x]Range[0, nn]!]] (* Harvey P. Dale, Aug 29 2012 *)
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PROG
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(PARI) my(x='x+O('x^30)); apply(numerator, Vec(serlaplace(exp(sqrt(1+x)-1)))) \\ Michel Marcus, Nov 30 2023
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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