A372424 a(n) is the numerator of the expected number of nodes of the tree representing the process of eliminating from n people a random group by tossing coins, and repeating this process recursively until a single loser is determined.

1, 4, 29, 116, 1921, 7142, 819929, 27378104, 809502167, 12262145758, 884553827, 293505915894364, 411130294447236989, 492490763456121568802, 34616266418646612178979, 666352599638002441306192, 871949152921567211061873859, 12914302458440850210396508294466, 94217989024368593164211326506247657

Offset

1,2

Comments

See A372422 for more information.

Links

Table of n, a(n) for n=1..19.

Example

a(n)/A372425(n): 1, 4, 29/6, 116/21, 1921/315, 7142/1085, 819929/117180, 27378104/3720465, 809502167/105413175, 12262145758/1539032355, ...
Approximately 1.0, 4.0, 4.8333, 5.5238, 6.0984, 6.5825, 6.9972, 7.3588, 7.6793, 7.9674, 8.2293, 8.4695, 8.6914, 8.8975, 9.0900, ...

Prog

(PARI) a372424_5(N) = {1 + sum (k=1, N-1, 2*binomial(N, k) * bernfrac(k+1) /((1-1/2^k)*(k+1))) + sum (k=1, N-1, 2*binomial(N, k) * bernfrac(k+1) / (k+1)) - sum (k=1, N-1, binomial(N, k) * bernfrac(k) / (1-1/2^k))};
a372424(n) = numerator(a372424_5(n))

Crossrefs

A372425 are the corresponding denominators.

Sequence in context: A295842 A345897 A368372 * A095670 A370435 A353972

Adjacent sequences: A372421 A372422 A372423 * A372425 A372426 A372427

Keyword

nonn,frac

Author

Hugo Pfoertner, May 03 2024

Status

approved