OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..403
FORMULA
Numerators of coefficients in expansion of sqrt(Pi*x*exp(-x)/2) * erfi(sqrt(x/2)) / (1 - x).
EXAMPLE
1, 2/3, 11/15, 76/105, 137/189, 7534/10395, 97943/135135, 1469144/2027025, 24975449/34459425, ...
MAPLE
S:= 0: R:= NULL:
for n from 1 to 100 do
S:= S + (-1)^(n+1)/doublefactorial(2*n-1);
R:= R, numer(S);
od:
R; # Robert Israel, Jan 10 2024
MATHEMATICA
Table[Sum[(-1)^(k + 1)/(2 k - 1)!!, {k, 1, n}], {n, 1, 21}] // Numerator
nmax = 21; CoefficientList[Series[Sqrt[Pi x Exp[-x]/2] Erfi[Sqrt[x/2]]/(1 - x), {x, 0, nmax}], x] // Numerator // Rest
Table[1/(1 + ContinuedFractionK[2 k - 1, 2 k, {k, 1, n - 1}]), {n, 1, 21}] // Numerator
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, May 23 2022
STATUS
approved