A011001 -id:A011001 - cp's OEIS frontend

A017770 Binomial coefficients C(54,n).

1, 54, 1431, 24804, 316251, 3162510, 25827165, 177100560, 1040465790, 5317936260, 23930713170, 95722852680, 343006888770, 1108176102180, 3245372870670, 8654327655120, 21094923659355, 47153358767970, 96926348578605, 183649923622620, 321387366339585

Offset: 0

N. J. A. Sloane

Row 54 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..54 (full sequence)

Cf. A010926-A011001, A017765-A017769, A017771-A017816.

[Binomial(54,n): n in [0..54]]; // G. C. Greubel, Nov 13 2018

seq(binomial(54,n), n=0..54); # Nathaniel Johnston, Jun 24 2011

Binomial[54,Range[0,54]] (* G. C. Greubel, Nov 13 2018 *)

vector(54, n, n--; binomial(54,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(54, n) for n in range(55)] # Zerinvary Lajos, May 23 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^54.
E.g.f.: 1F1(-54; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017771 Binomial coefficients C(55,n).

Original entry on oeis.org

1, 55, 1485, 26235, 341055, 3478761, 28989675, 202927725, 1217566350, 6358402050, 29248649430, 119653565850, 438729741450, 1451182990950, 4353548972850, 11899700525790, 29749251314475, 68248282427325, 144079707346575, 280576272201225, 505037289962205

Offset: 0

N. J. A. Sloane

Row 55 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..55 (full sequence)

Cf. A010926-A011001, A017765-A017770, A017772-A017816.

[Binomial(55,n): n in [0..55]]; // G. C. Greubel, Nov 13 2018

seq(binomial(55,n), n=0..55); # Nathaniel Johnston, Jun 24 2011

Binomial[55,Range[0,55]] (* Harvey P. Dale, Feb 26 2013 *)

vector(55, n, n--; binomial(55,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(55, n) for n in range(56)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^55.
E.g.f.: 1F1(-55; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017772 Binomial coefficients C(56,n).

Original entry on oeis.org

1, 56, 1540, 27720, 367290, 3819816, 32468436, 231917400, 1420494075, 7575968400, 35607051480, 148902215280, 558383307300, 1889912732400, 5804731963800, 16253249498640, 41648951840265, 97997533741800, 212327989773900, 424655979547800, 785613562163430

Offset: 0

N. J. A. Sloane

Row 56 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..56 (full sequence)

Cf. A010926-A011001, A017765-A017771, A017773-A017816.

[Binomial(56,n): n in [0..56]]; // G. C. Greubel, Nov 13 2018

seq(binomial(56,n), n=0..56); # Nathaniel Johnston, Jun 24 2011

Binomial[56,Range[0,20]] (* Harvey P. Dale, Sep 05 2013 *)

vector(56, n, n--; binomial(56,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(56, n) for n in range(57)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^56.
E.g.f.: 1F1(-56; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017773 Binomial coefficients C(57,n).

Original entry on oeis.org

1, 57, 1596, 29260, 395010, 4187106, 36288252, 264385836, 1652411475, 8996462475, 43183019880, 184509266760, 707285522580, 2448296039700, 7694644696200, 22057981462440, 57902201338905, 139646485582065, 310325523515700, 636983969321700

Offset: 0

N. J. A. Sloane

Row 57 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..57 (full sequence)

Cf. A010926-A011001, A017765-A017772, A017774-A017816.

[Binomial(57,n): n in [0..57]]; // G. C. Greubel, Nov 13 2018

seq(binomial(57,n), n=0..57); # Nathaniel Johnston, Jun 24 2011

Binomial[57, Range[0,57]] (* G. C. Greubel, Nov 13 2018 *)

vector(57, n, n--; binomial(57,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(57, n) for n in range(58)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^57.
E.g.f.: 1F1(-57; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017774 Binomial coefficients C(58,n).

Original entry on oeis.org

1, 58, 1653, 30856, 424270, 4582116, 40475358, 300674088, 1916797311, 10648873950, 52179482355, 227692286640, 891794789340, 3155581562280, 10142940735900, 29752626158640, 79960182801345, 197548686920970, 449972009097765, 947309492837400

Offset: 0

N. J. A. Sloane

Row 58 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..58 (full sequence)

Cf. A010926-A011001, A017765-A017773, A017775-A017816.

[Binomial(58,n): n in [0..58]]; // G. C. Greubel, Nov 13 2018

seq(binomial(58,n), n=0..58); # Nathaniel Johnston, Jun 24 2011

Binomial[58, Range[0,58]] (* or *) With[{nmax = 58}, CoefficientList[ Series[Hypergeometric1F1[-58, 1, -x], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Nov 13 2018 *)

vector(58, n, n--; binomial(58,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(58, n) for n in range(18)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^58.
E.g.f.: 1F1(-58; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017775 Binomial coefficients C(59,n).

Original entry on oeis.org

1, 59, 1711, 32509, 455126, 5006386, 45057474, 341149446, 2217471399, 12565671261, 62828356305, 279871768995, 1119487075980, 4047376351620, 13298522298180, 39895566894540, 109712808959985, 277508869722315, 647520696018735, 1397281501935165

Offset: 0

N. J. A. Sloane

Row 59 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..59 (full sequence)

Cf. A010926-A011001, A017765-A017774, A017776-A017816.

[Binomial(59,n): n in [0..59]]; // G. C. Greubel, Nov 13 2018

seq(binomial(59,n), n=0..59); # Nathaniel Johnston, Jun 24 2011

Binomial[59,#]&/@Range[0,20]  (* Harvey P. Dale, Mar 06 2011 *)

vector(59, n, n--; binomial(59,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(59, n) for n in range(18)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^59.
E.g.f.: 1F1(-59; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017776 Binomial coefficients C(60,n).

Original entry on oeis.org

1, 60, 1770, 34220, 487635, 5461512, 50063860, 386206920, 2558620845, 14783142660, 75394027566, 342700125300, 1399358844975, 5166863427600, 17345898649800, 53194089192720, 149608375854525, 387221678682300, 925029565741050, 2044802197953900

Offset: 0

N. J. A. Sloane

Row 60 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..60 (full sequence)

Cf. A010926-A011001, A017765-A017775, A017777-A017816.

[Binomial(60,n): n in [0..60]]; // G. C. Greubel, Nov 13 2018

seq(binomial(60,n), n=0..60); # Nathaniel Johnston, Jun 24 2011

Binomial[60, Range[0,60]] (* G. C. Greubel, Nov 13 2018 *)

vector(60, n, n--; binomial(60,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(60, n) for n in range(18)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^60.
E.g.f.: 1F1(-60; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017777 Binomial coefficients C(61,n).

Original entry on oeis.org

1, 61, 1830, 35990, 521855, 5949147, 55525372, 436270780, 2944827765, 17341763505, 90177170226, 418094152866, 1742058970275, 6566222272575, 22512762077400, 70539987842520, 202802465047245, 536830054536825, 1312251244423350, 2969831763694950

Offset: 0

N. J. A. Sloane

Row 61 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..61 (full sequence)

Cf. A010926-A011001, A017765-A017776, A017778-A017816.

[Binomial(61,n): n in [0..61]]; // G. C. Greubel, Nov 13 2018

seq(binomial(61,n), n=0..61); # Nathaniel Johnston, Jun 24 2011

Binomial[61, Range[0,61]] (* G. C. Greubel, Nov 13 2018 *)

vector(61, n, n--; binomial(61,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(61, n) for n in range(18)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^61.
E.g.f.: 1F1(-61; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017778 Binomial coefficients C(62,n).

Original entry on oeis.org

1, 62, 1891, 37820, 557845, 6471002, 61474519, 491796152, 3381098545, 20286591270, 107518933731, 508271323092, 2160153123141, 8308281242850, 29078984349975, 93052749919920, 273342452889765, 739632519584070, 1849081298960175, 4282083008118300

Offset: 0

N. J. A. Sloane

Row 62 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..62 (full sequence)

Cf. A010926-A011001, A017765-A017777, A017779-A017816.

[Binomial(62,n): n in [0..62]]; // G. C. Greubel, Nov 14 2018

seq(binomial(62,n), n=0..62); # Nathaniel Johnston, Jun 24 2011

Binomial[62, Range[0,62]] (* G. C. Greubel, Nov 14 2018 *)
CoefficientList[Series[(1+x)^62,{x,0,20}],x] (* Harvey P. Dale, Aug 11 2024 *)

vector(62, n, n--; binomial(62,n)) \\ G. C. Greubel, Nov 14 2018

[binomial(62, n) for n in range(18)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 14 2018: (Start)
G.f.: (1+x)^62.
E.g.f.: 1F1(-62; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017779 Binomial coefficients C(63,n).

Original entry on oeis.org

1, 63, 1953, 39711, 595665, 7028847, 67945521, 553270671, 3872894697, 23667689815, 127805525001, 615790256823, 2668424446233, 10468434365991, 37387265592825, 122131734269895, 366395202809685, 1012974972473835, 2588713818544245, 6131164307078475

Offset: 0

N. J. A. Sloane

Row 63 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..63 (full sequence)

Cf. A010926-A011001, A017765-A017778, A017780-A017816.

[Binomial(63,n): n in [0..63]]; // G. C. Greubel, Nov 14 2018

seq(binomial(63,n), n=0..63); # Nathaniel Johnston, Jun 24 2011

Binomial[63, Range[0,63]] (* G. C. Greubel, Nov 14 2018 *)

vector(63, n, n--; binomial(63,n)) \\ G. C. Greubel, Nov 14 2018

[binomial(63, n) for n in range(18)] # Zerinvary Lajos, May 28 2009

From G. C. Greubel, Nov 14 2018: (Start)
G.f.: (1+x)^63.
E.g.f.: 1F1(-63; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

cp's OEIS Frontend

A017770 Binomial coefficients C(54,n).

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A017771 Binomial coefficients C(55,n).

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A017772 Binomial coefficients C(56,n).

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Magma

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A017773 Binomial coefficients C(57,n).

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Magma

Maple

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PARI

Sage

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A017774 Binomial coefficients C(58,n).

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Magma

Maple

Mathematica

PARI

Sage

Formula

A017775 Binomial coefficients C(59,n).

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Magma