OFFSET
1,2
FORMULA
Numerators of coefficients in expansion of (gamma + log(x) - Ei(-x)) / (1 - x), x > 0.
EXAMPLE
1, 3/4, 29/36, 229/288, 5737/7200, 8603/10800, 210781/264600, ...
MATHEMATICA
Table[Sum[(-1)^(k + 1)/(k k!), {k, 1, n}], {n, 1, 20}] // Numerator
nmax = 20; Assuming[x > 0, CoefficientList[Series[(EulerGamma + Log[x] - ExpIntegralEi[-x])/(1 - x), {x, 0, nmax}], x]] // Numerator // Rest
PROG
(PARI) a(n) = numerator(sum(k=1, n, (-1)^(k+1)/(k*k!))); \\ Michel Marcus, May 26 2022
(Python)
from math import factorial
from fractions import Fraction
def A354402(n): return sum(Fraction(1 if k & 1 else -1, k*factorial(k)) for k in range(1, n+1)).numerator # Chai Wah Wu, May 27 2022
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, May 25 2022
STATUS
approved