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A114604 Numerator of partial sums of A005329/A006125. 2
1, 5, 43, 709, 23003, 1481957, 190305691, 48796386661, 25003673060507, 25613941912987493, 52467767892904362139, 214929296497738201165669, 1760788099067877263041671323, 28849467307107603960961499533157 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

To win a game, you must flip n+1 heads in a row, where n is the total number of tails flipped so far. The probability of having won before n+1 tails (that is, winning by flipping n+1 or fewer heads in a row) is a(n)/A006125(n). The probability of winning for the first time after n tails (that is, by flipping n+1 heads in a row) is A005329(n)/A006125(n).

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = numerator(Sum_{k=0..n} A005329(k)/A006125(k)).

a(n) = a(n-1) * 2^(n+1) + A005329(n).

EXAMPLE

a(3) = 43 because 1/2 + 1/8 + 3/64 = 43/64, or because a(2) * 2^(2+1) + A005329(2) = 5 * 8 + 3 = 43.

CROSSREFS

Cf. A005329, A006125.

Sequence in context: A280776 A255895 A160450 * A085098 A271679 A099794

Adjacent sequences:  A114601 A114602 A114603 * A114605 A114606 A114607

KEYWORD

easy,frac,nonn

AUTHOR

Joshua Zucker, Dec 14 2005

STATUS

approved

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Last modified December 5 00:34 EST 2020. Contains 338943 sequences. (Running on oeis4.)