A376053
Numerator of the sum S(n) defined in A376052.
Original entry on oeis.org
1, 8, 71, 248, 3043, 43024, 89051, 764441, 451021514, 25508567769, 411827311870583771, 525058386770138717020639964821, 528134692562568161116953143877712480332943632586669596859, 2267693117789905604207315326366543773113615946806750184592188584359364943382168221068055512231683584106110223751
Offset: 1
The initial values of S(n) are 1/3, 8/15, 71/105, 248/315, 3043/3465, 43024/45045, 89051/90090, ...
A376054
Denominator of sum S(n) defined in A376052.
Original entry on oeis.org
3, 15, 105, 315, 3465, 45045, 90090, 765765, 451035585, 25508568085, 411827311870584610, 525058386770138717020639964850, 528134692562568161116953143877712480332943632586669596900
Offset: 1
The initial values of S(n) are 1/3, 8/15, 71/105, 248/315, 3043/3465, 43024/45045, 89051/90090, ...
A376059
a(n) is the denominator of the sum S(n) defined in A376058.
Original entry on oeis.org
1, 2, 6, 78, 18330, 1679962830, 22578200883132834030, 6627077016548303724729207245056971365730, 922281145448518091883798423085535218757314338662318933097843039655721026758456630
Offset: 0
The first few values of S(n) are 0, 1/2, 5/6, 77/78, 18329/18330, 1679962829/1679962830, 22578200883132834029/22578200883132834030, ...
-
RecurrenceTable[{a[n+1] == Fibonacci[n+1]*a[n]^2 + a[n], a[0] == 1}, a, {n, 0, 8}] (* Amiram Eldar, Sep 15 2024 *)
A376184
Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} b(k)/a(k) < 1, where {b(k)} is the sequence b(1)=5/4, b(2*i)=3/2, b(2*i+1)=6/5 (i>0).
Original entry on oeis.org
2, 5, 17, 341, 92753, 10753782821, 92515075960384748177, 10698799099944699918936107506299150093941, 91571441744782016867976366392607084634231243149599342901251284090792487979854033
Offset: 1
The initial values of S(n) are 5/8, 37/40, 677/680, 231877/231880, 21507565637/21507565640, 231287689900961870437/231287689900961870440, ...
A376185
a(n) = denominator of the sum S(n) defined in A376062.
Original entry on oeis.org
12, 48, 624, 97968, 2399530224, 1439436326371902768, 517994234419759747473589427583418224, 67079506723028253472357256785558488997471406450171845011442457607246768
Offset: 1
The initial values of S(n) are 7/12, 43/48, 619/624, 97963/97968, 2399530219/2399530224, 1439436326371902763/1439436326371902768 ...
A376186
a(n) = denominator of the sum S(n) defined in A376184.
Original entry on oeis.org
8, 40, 680, 231880, 21507565640, 231287689900961870440, 21397598199889399837872215012598300187880, 228928604361955042169940915981517711585578107873998357253128210226981219949635080
Offset: 1
The initial values of S(n) are 5/8, 37/40, 677/680, 231877/231880, 21507565637/21507565640, 231287689900961870437/231287689900961870440, ...
Cf.
A004168,
A082732,
A374663,
A375516,
A375531,
A375532,
A375781,
A375522,
A376048-
A376062,
A376184,
A376185.
A375528
a(n) = denominator of Sum_{k = 1..n} 1 / (A000959(k)*A375527(k)).
Original entry on oeis.org
1, 2, 6, 42, 630, 57330, 219172590, 2287458514758690, 523246645674205487113407810300, 34223381526163442974989472671319545640510650941743506071550, 65068880171408068403202506207461768112305307530373013598603234255112994800902512713302330140957468591804616490482800
Offset: 1
A376060
Lexicographically earliest sequence of positive integers a(0), a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 0..n-1} Catalan(k)/a(k) < 1.
Original entry on oeis.org
2, 3, 13, 391, 426973, 546916547269, 940084230410591812263433, 2872214670866692695441731060944339347071024216683
Offset: 0
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