A274983
a(n) = [n]phi! + [n]{1-phi}!, where [n]_q! is the q-factorial, phi = (1+sqrt(5))/2.
Original entry on oeis.org
2, 2, 3, 14, 130, 2120, 58120, 2636360, 196132320, 23805331920, 4698862837680, 1505416321070640, 781888977967152000, 657866357975539785600, 896265744457831561756800, 1976607903479486428467148800, 7055269158071576119808840371200
Offset: 0
For n = 3, [3]_phi! = 1060 + 474*sqrt(5), so a(5) = 2*1060 = 2120 and A274985(5) = 2*474 = 948.
-
Round@Table[QFactorial[n, GoldenRatio] + QFactorial[n, 1 - GoldenRatio], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
A274985
a(n) = ([n]phi! - [n]{1-phi}!)/sqrt(5), where [n]_q! is the q-factorial, phi = (1+sqrt(5))/2.
Original entry on oeis.org
0, 0, 1, 6, 58, 948, 25992, 1179016, 87713040, 10646068080, 2101395344400, 673242645670320, 349671381118477440, 294206779308703578240, 400822226102433353285760, 883965927408694948620295680, 3155212287401150653204012531200
Offset: 0
For n = 3, [3]_phi! = 1060 + 474*sqrt(5), so A274983(5) = 2*1060 = 2120 and a(5) = 2*474 = 948.
-
Round@Table[(QFactorial[n, GoldenRatio] - QFactorial[n, 1 - GoldenRatio])/Sqrt[5], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
A276475
a(n) = ((sqrt(2); sqrt(2))_n - (-sqrt(2); -sqrt(2))_n)/(2*sqrt(2)), where (q; q)_n is the q-Pochhammer symbol.
Original entry on oeis.org
0, -1, 1, 3, -9, -69, 483, 5355, -80325, -2081205, 64517355, 2738408715, -172519749045, -17158004483445, 2179066569397515, 365466952872801675, -93194072982564427125, -36694334101466364023925, 18750804725849312016225675
Offset: 0
-
Round@Table[(QPochhammer[Sqrt[2], Sqrt[2], n] - QPochhammer[-Sqrt[2], -Sqrt[2], n])/(2 Sqrt[2]), {n, 0, 20}]
A276990
a(n) = (phi; phi)_n + (1-phi; 1-phi)_n, where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio.
Original entry on oeis.org
2, 1, 2, -2, 20, -190, 3240, -90800, 4174920, -313173840, 38204662320, -7564715117520, 2428250059593600, -1262694691720176000, 1063187432567808662400, -1449125250052431355430400, 3196769645011428154428883200, -11412468527893653264760022630400
Offset: 0
-
Round@Table[QPochhammer[GoldenRatio, GoldenRatio, n] + QPochhammer[1 - GoldenRatio, 1 - GoldenRatio, n], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
A276991
a(n) = ((phi; phi)_n - (1-phi; 1-phi)_n)/sqrt(5), where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio.
Original entry on oeis.org
0, -1, 0, -2, 8, -86, 1448, -40608, 1867080, -140055600, 17085644400, -3383043446640, 1085946439923840, -564694233102890880, 475471874409018791040, -648068513405723438730240, 1429638846930684965104992000, -5103811083889432701541321459200
Offset: 0
-
Round@Table[(QPochhammer[GoldenRatio, GoldenRatio, n] - QPochhammer[1 - GoldenRatio, 1 - GoldenRatio, n])/Sqrt[5], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
Showing 1-5 of 5 results.
Comments