A226931 Numerator of n + Sum(binomial(n,k)*(k/n)^k*((n-k)/n)^(n-k), k=0..n).

3, 9, 53, 231, 5319, 3167, 1296273, 1604979, 64370707, 22906587, 411169704813, 610433321, 424312831956207, 2146177886409, 98731231639051, 12218411169233691, 1112291237880234922707, 2196818399875253, 2619031544578888560315813, 16827894135040576041

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Helmut Prodinger, An identity conjectured by Lacasse via the tree function, Electronic Journal of Combinatorics, 20(3) (2013), #P7. See xi_2(n).

Example

3, 9/2, 53/9, 231/32, 5319/625, 3167/324, 1296273/117649, 1604979/131072, ...

Prog

(PARI) a(n) = numerator(n + sum(k=0, n, binomial(n, k)*(k/n)^k*((n-k)/n)^(n-k))); \\ Michel Marcus, Jun 11 2015

Crossrefs

Denominators are in A036505. Cf. A090878, A063170.

Sequence in context: A018966 A109933 A018477 * A013341 A077795 A038496

Adjacent sequences: A226928 A226929 A226930 * A226932 A226933 A226934

Keyword

nonn,frac

Author

N. J. A. Sloane, Jul 31 2013

Status

approved