A354404 a(n) is the denominator of Sum_{k=1..n} (-1)^(k+1) / (k*k!).

1, 4, 36, 288, 7200, 10800, 264600, 33868800, 914457600, 4572288000, 553246848000, 2212987392000, 373994869248000, 327245510592000, 19634730635520000, 5026491042693120000, 1452655911338311680000, 39221709606134415360000, 14159037167814523944960000, 141590371678145239449600000

Offset: 1

Author

Ilya Gutkovskiy, May 25 2022

Keywords

• nonn
• frac

Examples

			1, 3/4, 29/36, 229/288, 5737/7200, 8603/10800, 210781/264600, ...
		

Crossrefs

Cf. A001563, A053556, A061355, A239069, A354401, A354402 (numerators).

Programs

Mathematica

Table[Sum[(-1)^(k + 1)/(k k!), {k, 1, n}], {n, 1, 20}] // Denominator
nmax = 20; Assuming[x > 0, CoefficientList[Series[(EulerGamma + Log[x] - ExpIntegralEi[-x])/(1 - x), {x, 0, nmax}], x]] // Denominator // Rest

PARI

a(n) = denominator(sum(k=1, n, (-1)^(k+1)/(k*k!))); \\ Michel Marcus, May 26 2022

Python

from math import factorial
from fractions import Fraction
def A354404(n): return sum(Fraction(1 if k & 1 else -1, k*factorial(k)) for k in range(1,n+1)).denominator # Chai Wah Wu, May 27 2022

Formula

Denominators of coefficients in expansion of (gamma + log(x) - Ei(-x)) / (1 - x), x > 0.