A354401 a(n) is the denominator of Sum_{k=1..n} 1 / (k*k!).

1, 4, 36, 288, 7200, 10800, 66150, 33868800, 914457600, 4572288000, 553246848000, 737662464000, 41554985472000, 54540918432000, 19634730635520000, 5026491042693120000, 1452655911338311680000, 39221709606134415360000, 14159037167814523944960000, 141590371678145239449600000

Offset: 1

Author

Ilya Gutkovskiy, May 25 2022

Keywords

• nonn
• frac

Examples

			1, 5/4, 47/36, 379/288, 9487/7200, 14233/10800, 87179/66150, ...
		

Crossrefs

Cf. A001563, A053556, A061355, A229837, A353545 (numerators), A354404.

Programs

Mathematica

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

PARI

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

Python

from math import factorial
from fractions import Fraction
def A354401(n): return sum(Fraction(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 (Ei(x) - log(x) - gamma) / (1 - x), x > 0.