A295431 -id:A295431 - cp's OEIS frontend

A295435 a(n) = (12n)!(3n)!/((6n)!(5n)!(4n)!).

1, 1386, 6374082, 33660501840, 188276393811330, 1087036407409838886, 6403774152656100209808, 38253942248288803868931624, 230861076790453965336241603458, 1404158783195280855598258861670940, 8593283348445510533260633624776561582, 52853021730805678055150543201466838900800

Offset: 0

Gheorghe Coserea, Nov 23 2017

nonn

Cf. A295431.

Array[(12 #)!*(3 #)!/((6 #)!*(5 #)!*(4 #)!) &, 12, 0] (* Michael De Vlieger, Nov 23 2017 *)
CoefficientList[ Series[ HypergeometricPFQ[{1/12, 1/3, 5/12, 7/12, 2/3, 11/12}, {1/5, 2/5, 1/2, 3/5, 4/5}, 20155392/3125 x], {x, 0, 11}], x] (* Robert G. Wilson v, Nov 23 2017 *)

G.f.: hypergeom([1/12, 1/3, 5/12, 7/12, 2/3, 11/12], [1/5, 2/5, 1/2, 3/5, 4/5], 20155392/3125*x).

a(n) ~ 2^(10*n-1) * 3^(9*n + 1/2) / (5^(5*n + 1/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

A295438 a(n) = (9n)!(2n)!/((6n)!(4n)!*n!).

Original entry on oeis.org

1, 42, 3978, 426075, 48141450, 5605430292, 665398273995, 80056334499603, 9727795137150090, 1191070745968697880, 146715992699777718228, 18161051595569811828018, 2257160798030399890529355, 281490217405724159448825420, 35206768357722972409203943875, 4414468429202421653755921429200

Offset: 0

Gheorghe Coserea, Nov 23 2017

nonn

Cf. A295431.

f[n_] := (9n)! (2n)!/((6n)!*(4n)! n!); Array[f, 16, 0] (* or *)
CoefficientList[ Series[ HypergeometricPFQ[{1/9, 2/9, 4/9, 5/9, 7/9, 8/9}, {1/6, 1/4, 1/2, 3/4, 5/6}, 531441/4096 x], {x, 0, 15}], x] (* Robert G. Wilson v, Nov 23 2017 *)

G.f.: hypergeom([1/9, 2/9, 4/9, 5/9, 7/9, 8/9], [1/6, 1/4, 1/2, 3/4, 5/6], 531441/4096*x).

a(n) ~ 3^(12*n + 1/2) / (sqrt(Pi*n) * 2^(12*n + 3/2)). - Vaclav Kotesovec, Apr 03 2025

A295440 a(n) = (18n)!(4n)!(3n)!/((9n)!(8n)!(6n)!(2n)!).

Original entry on oeis.org

1, 43758, 7012604550, 1288415796384780, 250622090889055155270, 50312973039218473430585508, 10304958075870392958137083227804, 2140123855549810059379592073872919000, 449006091012360080585628994760351491412550, 94939602104589721712783038933265704553286808500

Offset: 0

Gheorghe Coserea, Nov 23 2017

nonn

Cf. A295431.

f[n_] := (18n)! (4n)! (3n)!/((9n)! (8n)! (6n)! (2n)!); Array[f, 10, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/8, 3/8, 1/2, 5/8, 7/8}, 14348907/64 x], {x, 0, 9}], x] (* Robert G. Wilson v, Nov 23 2017 *)

G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/8, 3/8, 1/2, 5/8, 7/8], 14348907/64*x).
D-finite with recurrence n*(8*n-5)*(8*n-3)*(8*n-1)*(2*n-1)*(8*n-7)*a(n) -54*(18*n-11)*(18*n-7)*(18*n-17)*(18*n-13)*(18*n-5)*(18*n-1)*a(n-1)=0. - R. J. Mathar, Jan 13 2025
a(n) ~ 3^(15*n) / (2^(6*n + 3/2) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

A295442 a(n) = (18n)!(5n)!(3n)!/((10n)!(9n)!(6n)!*n!).

Original entry on oeis.org

1, 4862, 65132550, 987291797996, 15789207515217990, 260227401685879140612, 4372592850984736084611996, 74468439316740019538310543000, 1280895791499708481382281179968070, 22200471460266930185258813786107130900, 387105235604016899402464538876438270501300

Offset: 0

Gheorghe Coserea, Nov 23 2017

nonn

Cf. A295431.

f[n_] := (18n)! (5n)! (3n)!/((10n)! (9n)! (6n)! n!); Array[f, 11, 0] (* or *)CoefficientList[ Series[ HypergeometricPFQ[{1/18, 5/18, 7/18, 11/18, 13/18, 17/18}, {1/10, 3/10, 1/2, 7/10, 9/10}, 57395628/3125 x], {x, 0, 10}], x] (* Robert G. Wilson v, Nov 23 2017 *)

G.f.: hypergeom([1/18, 5/18, 7/18, 11/18, 13/18, 17/18], [1/10, 3/10, 1/2, 7/10, 9/10], 57395628/3125*x).

a(n) ~ 2^(2*n-1) * 3^(15*n) / (5^(5*n) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 11 2025

A295445 a(n) = (18n)!(2n)!/((9n)!(6n)!(5n)!).

Original entry on oeis.org

1, 408408, 802241960520, 1823169705017624880, 4396944340992842923469640, 10954213672604884898541157653408, 27856219773497860095974794307896603536, 71846723613356502547294848257330357588794200, 187234481335648875117449455455153824826269008835400

Offset: 0

Gheorghe Coserea, Nov 27 2017

nonn

Cf. A295431.

G.f.: hypergeom([1/18, 5/18, 7/18, 1/2, 11/18, 13/18, 17/18], [1/5, 1/3, 2/5, 3/5, 2/3, 4/5], 8707129344/3125*x).

A295456 a(n) = (30n)!(5n)!(4n)!/((15n)!(12n)!(10n)!(2n)!).

Original entry on oeis.org

1, 168043980, 126694219977836700, 109504706026534324525391988, 100204869963549181630558779565943580, 94632263448378916462441320194245442445186480, 91178760822805067678742350221792424866578707819103300, 89078657321704573467701346299333700225381618490806719145843000

Offset: 0

Gheorghe Coserea, Nov 27 2017

nonn

Cf. A295431.

G.f.: hypergeom([1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30], [1/12, 1/3, 5/12, 1/2, 7/12, 2/3, 11/12], 1054687500*x).

A295458 a(n) = (30n)!(5n)!(4n)!/((15n)!(10n)!(8n)!(6n)!).

Original entry on oeis.org

1, 5545451340, 188242272043069768860, 7383354803839076831124554790900, 307213802011837003346320048243705086348060, 13202980048704429908831487095516759161045931997393840, 579138708444140353944173816622205024638976091097557185100664900

Offset: 0

Gheorghe Coserea, Nov 28 2017

nonn

Cf. A295431.

G.f.: hypergeom([1/30, 7/30, 11/30, 13/30, 17/30, 19/30, 23/30, 29/30], [1/8, 1/3, 3/8, 1/2, 5/8, 2/3, 7/8], 192216796875/4*x).

A295459 a(n) = (15n)!(2n)!/((10n)!(4n)!(3n)!).

Original entry on oeis.org

1, 5005, 90135045, 1868031888580, 41029265920459845, 930412757112634271880, 21530356169879586359196900, 505246886354870326510495672020, 11978661740397444504877351546799685, 286230481407830055989299003347834843760, 6881913823453630116611423770861944135246920

Offset: 0

Gheorghe Coserea, Nov 28 2017

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..227

Cf. A295431.

Table[((15n)!(2n)!)/((10n)!(4n)!(3n)!),{n,0,20}] (* Harvey P. Dale, Apr 02 2024 *)

G.f.: hypergeom([1/15, 2/15, 4/15, 7/15, 8/15, 11/15, 13/15, 14/15], [1/10, 1/4, 3/10, 1/2, 7/10, 3/4, 9/10], 1660753125/65536*x).

A295469 a(n) = (20n)!(3n)!/((12n)!(10n)!*n!).

Original entry on oeis.org

1, 8398, 194588550, 5100249334348, 141026130105441350, 4018577033905015730148, 116743212747975158088926364, 3437433902477818949422435085400, 102221680117258170626629637553328710, 3063070065565412402561157982751304224500, 92339640658637142866394391974518333925957300

Offset: 0

Gheorghe Coserea, Nov 28 2017

nonn

Cf. A295431.

A295469 := proc(n)
    (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!) ;
end proc:
seq(A295469(n),n=0..43) ; # R. J. Mathar, Jul 27 2022

G.f.: hypergeom([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/12, 1/6, 5/12, 1/2, 7/12, 5/6, 11/12], 625000000/19683*x).

D-finite with recurrence +27*n*(12*n-11)*(12*n-1)*(6*n-1)*(12*n-5)*(2*n-1)*(12*n-7)*(6*n-5)*a(n) -50*(20*n-11)*(20*n-9)*(20*n-7)*(20*n-3)*(20*n-1)*(20*n-19)*(20*n-17)*(20*n-13)*a(n-1)=0. - R. J. Mathar, Jul 27 2022

A295470 a(n) = (20n)!(6n)!n!/((12n)!(10n)!(3n)!(2*n)!).

Original entry on oeis.org

1, 83980, 29966636700, 12398706131799988, 5447952226877283703580, 2473617870747229982625186480, 1146602219745194113307246953503300, 539110100779634346434520330628287843000, 256130864665265316470308479790547084791062300, 122657586881362583078239819278500645564891283341200

Offset: 0

Gheorghe Coserea, Nov 28 2017

nonn

Cf. A295431.

G.f.: hypergeom([1/20, 3/20, 7/20, 9/20, 11/20, 13/20, 17/20, 19/20], [1/12, 1/3, 5/12, 1/2, 7/12, 2/3, 11/12], 10000000000/19683*x).

cp's OEIS Frontend

A295435 a(n) = (12*n)!*(3*n)!/((6*n)!*(5*n)!*(4*n)!).

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A295438 a(n) = (9*n)!*(2*n)!/((6*n)!*(4*n)!*n!).

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A295440 a(n) = (18*n)!*(4*n)!*(3*n)!/((9*n)!*(8*n)!*(6*n)!*(2*n)!).

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Mathematica

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A295442 a(n) = (18*n)!*(5*n)!*(3*n)!/((10*n)!*(9*n)!*(6*n)!*n!).

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Mathematica

Formula

A295445 a(n) = (18*n)!*(2*n)!/((9*n)!*(6*n)!*(5*n)!).

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A295456 a(n) = (30*n)!*(5*n)!*(4*n)!/((15*n)!*(12*n)!*(10*n)!*(2*n)!).

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Formula

A295458 a(n) = (30*n)!*(5*n)!*(4*n)!/((15*n)!*(10*n)!*(8*n)!*(6*n)!).

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Crossrefs

Formula

A295459 a(n) = (15*n)!*(2*n)!/((10*n)!*(4*n)!*(3*n)!).

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Mathematica

Formula

A295469 a(n) = (20*n)!*(3*n)!/((12*n)!*(10*n)!*n!).

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Maple

Formula

A295470 a(n) = (20*n)!*(6*n)!*n!/((12*n)!*(10*n)!*(3*n)!*(2*n)!).

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Author

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Crossrefs

Formula

A295435 a(n) = (12n)!(3n)!/((6n)!(5n)!(4n)!).

A295438 a(n) = (9n)!(2n)!/((6n)!(4n)!*n!).

A295440 a(n) = (18n)!(4n)!(3n)!/((9n)!(8n)!(6n)!(2n)!).

A295442 a(n) = (18n)!(5n)!(3n)!/((10n)!(9n)!(6n)!*n!).

A295445 a(n) = (18n)!(2n)!/((9n)!(6n)!(5n)!).

A295456 a(n) = (30n)!(5n)!(4n)!/((15n)!(12n)!(10n)!(2n)!).

A295458 a(n) = (30n)!(5n)!(4n)!/((15n)!(10n)!(8n)!(6n)!).

A295459 a(n) = (15n)!(2n)!/((10n)!(4n)!(3n)!).

A295469 a(n) = (20n)!(3n)!/((12n)!(10n)!*n!).

A295470 a(n) = (20n)!(6n)!n!/((12n)!(10n)!(3n)!(2*n)!).