A372424 - OEIS

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

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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