A043300 Denominator of L(n) = (Sum_{k=1..n} k^n)/(Sum_{k=1..n-1} k^n).

1, 1, 49, 52, 20515, 7689, 1976849, 769072, 196573677, 1176564625, 2252928456427, 915495729492, 116920050750711, 202297407264253, 1206847874699507489, 1507470694179701824, 6945343389873635897155

Offset

2,3

Comments

L(n) has the amazing asymptotic development L(n) = e + c(1)/n + c(2)/n^2 + c(3)/n^3 + ... with c(1) = e*(e+1)/(2*(e-1)), c(2) = e*(11*e^3 + 3*e^2 - 51*e - 11)/(24*(e-1)^3), etc., where e = exp(1).

References

"A sequence convergent to Napier's Constant" by Alexandru Lupas from the University "Lucian Blaga" of Sibiu / e-mail: lupas(AT)jupiter.sibiu.ro

Links

Amiram Eldar, Table of n, a(n) for n = 2..388

Alexandru Lupas, A sequence convergent to Napier's Constant.

Mathematica

a[n_] := Denominator[Sum[k^n, {k, 1, n}]/Sum[k^n, {k, 1, n - 1}]]; Array[a, 17, 2] (* Amiram Eldar, May 14 2022 *)

Prog

(PARI) a(n) = denominator(sum(k = 1, n, k^n)/sum(k = 1, n-1, k^n)); \\ Michel Marcus, Nov 21 2013

Crossrefs

Cf. A001113, A043299 (numerators).

Sequence in context: A020276 A346805 A118073 * A304008 A305358 A140388

Adjacent sequences: A043297 A043298 A043299 * A043301 A043302 A043303

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Apr 04 2002

Status

approved