cp's OEIS Frontend

Empirical: a(n) = 20*a(n-1) - 70*a(n-2) + 228*a(n-3) - 276*a(n-4) + 392*a(n-5) - 196*a(n-6) + 144*a(n-7).

Empirical g.f.: 4*x*(5 + 49*x^2 - 11*x^3 + 85*x^4 - 13*x^5 + 36*x^6) / (1 - 20*x + 70*x^2 - 228*x^3 + 276*x^4 - 392*x^5 + 196*x^6 - 144*x^7). - Colin Barker, Aug 26 2018

Empirical: a(n) = 35*a(n-1) -347*a(n-2) +1689*a(n-3) -2986*a(n-4) -2311*a(n-5) +23532*a(n-6) -23864*a(n-7) -36468*a(n-8) +100464*a(n-9) +94080*a(n-10)

Empirical: a(n) = 56*a(n-1) -1098*a(n-2) +10776*a(n-3) -59038*a(n-4) +197135*a(n-5) -527776*a(n-6) +1780117*a(n-7) -5020078*a(n-8) +3603978*a(n-9) -19091082*a(n-10) +61460622*a(n-11) +49090018*a(n-12) +274177128*a(n-13) +105163104*a(n-14) +354022404*a(n-15) +28705280*a(n-16) +147891456*a(n-17) -1275168*a(n-18) +15980544*a(n-19)

Empirical: a(n) = 84*a(n-1) -2771*a(n-2) +49004*a(n-3) -526214*a(n-4) +3641009*a(n-5) -16632719*a(n-6) +48536326*a(n-7) -53423733*a(n-8) -313959977*a(n-9) +1729942603*a(n-10) -7086418537*a(n-11) +13780962535*a(n-12) +5231265096*a(n-13) -20279410782*a(n-14) +609579098232*a(n-15) +294855159788*a(n-16) +2331852968592*a(n-17) +7276333185488*a(n-18) +4826951354776*a(n-19) +18771064269632*a(n-20) +25683656373760*a(n-21) +16941876341184*a(n-22) +25615354625280*a(n-23) +22113238049280*a(n-24) +5504163840000*a(n-25)

Empirical: a(n) = 120*a(n-1) -6060*a(n-2) +173316*a(n-3) -3172287*a(n-4) +39656548*a(n-5) -352443358*a(n-6) +2297379936*a(n-7) -11353877196*a(n-8) +45067977530*a(n-9) -163575910944*a(n-10) +627001572604*a(n-11) -2683978430932*a(n-12) +10780238513518*a(n-13) -32948873206590*a(n-14) +77959459244560*a(n-15) -153434141519476*a(n-16) +1059262494852896*a(n-17) -2694841466898608*a(n-18) +12219509145685508*a(n-19) +11985467868644368*a(n-20) +94047496662754280*a(n-21) +94835829721618640*a(n-22) +1050524403777918000*a(n-23) +2113714471975471104*a(n-24) +5481174460069822848*a(n-25) +10535537672809153264*a(n-26) +27173919094636341472*a(n-27) +47704013358770735568*a(n-28) +67212912534846684448*a(n-29) +62342889733184689824*a(n-30) +49243871592902490976*a(n-31) +27263322225301218304*a(n-32) +12918679041553050240*a(n-33) +2921299068148297728*a(n-34) +856946059741420288*a(n-35) -327218428029860352*a(n-36) -16665963801149440*a(n-37) -24912329585756160*a(n-38) +4712255288340480*a(n-39) +807198452121600*a(n-40) +68097422131200*a(n-41)

Empirical: a(n) = (353/181440)*n^9 + (5/126)*n^8 + (12287/30240)*n^7 + (131/60)*n^6 + (64877/8640)*n^5 + (135/8)*n^4 + (998257/45360)*n^3 + (53933/2520)*n^2 + (3421/252)*n - 2 for n>1.

Conjectures from Colin Barker, Aug 26 2018: (Start)

G.f.: x*(64 + 360*x - 324*x^2 + 1883*x^3 - 3447*x^4 + 4386*x^5 - 3748*x^6 + 2193*x^7 - 825*x^8 + 182*x^9 - 18*x^10) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.

(End)

Empirical: a(n) = (3551/47900160)*n^12 + (89357/39916800)*n^11 + (787537/21772800)*n^10 + (54391/145152)*n^9 + (3628073/1451520)*n^8 + (219389/19200)*n^7 + (790310011/21772800)*n^6 + (11979533/145152)*n^5 + (26980967/217728)*n^4 + (119696723/907200)*n^3 + (46358119/831600)*n^2 + (56717/396)*n + 52 for n>2

Empirical: a(n) = (769/444787200)*n^15 + (781507/10897286400)*n^14 + (732989/444787200)*n^13 + (6062213/239500800)*n^12 + (4527293/15966720)*n^11 + (49818529/21772800)*n^10 + (300432343/21772800)*n^9 + (9176781683/152409600)*n^8 + (2072451091/10886400)*n^7 + (1971136933/4354560)*n^6 + (16020797923/19958400)*n^5 + (55454431657/59875200)*n^4 - (688455589/2402400)*n^3 - (18610604083/37837800)*n^2 + (69728249/15015)*n + 2530 for n>3

Empirical: a(n) = (42587101/1600593426432000)*n^18 + (23341517/16167610368000)*n^17 + (15783371/356638464000)*n^16 + (31606091/33965568000)*n^15 + (17663092277/1207084032000)*n^14 + (133630090943/747242496000)*n^13 + (3090381263819/1810626048000)*n^12 + (861240248921/67060224000)*n^11 + (16435251844841/219469824000)*n^10 + (3455775661663/10450944000)*n^9 + (654929669980007/603542016000)*n^8 + (1738593710779/653184000)*n^7 + (82071435647381/16717428000)*n^6 + (429177771626699/59439744000)*n^5 - (15320544442081/40864824000)*n^4 - (2761354550633/92664000)*n^3 - (36294722496521/593762400)*n^2 + (776634903133/6126120)*n + 95040 for n>4

Empirical: a(n) = (3642102403/12772735542927360000)*n^21 + (1828819507/93573154160640000)*n^20 + (69800896237/91233825306624000)*n^19 + (267473506319/12804747411456000)*n^18 + (13894779382807/32011868528640000)*n^17 + (30522003341/4269957120000)*n^16 + (2960783594047/30893806944000)*n^15 + (396044918673407/376610217984000)*n^14 + (53677409656497673/5649153269760000)*n^13 + (20242631281245749/289700167680000)*n^12 + (2982742874548721/7242504192000)*n^11 + (1737409609193009/919683072000)*n^10 + (258559348958260442861/39544072888320000)*n^9 + (593900455377212143/36212520960000)*n^8 + (3978525082857841027/141228831744000)*n^7 + (1946054065487953843/47076277248000)*n^6 + (49893145987491754499/666913927680000)*n^5 - (383268963922742041/1984862880000)*n^4 - (252880325219600223869/123193822752000)*n^3 - (154838552783847197/36664828200)*n^2 + (12390598682741/2909907)*n + 3399959 for n>5