A010926 -id:A010926 - cp's OEIS frontend

A017765 Binomial coefficients C(49,n).

1, 49, 1176, 18424, 211876, 1906884, 13983816, 85900584, 450978066, 2054455634, 8217822536, 29135916264, 92263734836, 262596783764, 675248872536, 1575580702584, 3348108992991, 6499270398159, 11554258485616, 18851684897584, 28277527346376

Offset: 0

N. J. A. Sloane

Row 49 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..49 (full sequence)

Cf. A010926-A011001, A017766-A017816.

[Binomial(49,n): n in [0..49]]; // G. C. Greubel, Nov 13 2018

seq(binomial(49,n), n=0..49); # Nathaniel Johnston, Jun 24 2011

Binomial[49,Range[0,50]] (* Harvey P. Dale, Feb 17 2015 *)

vector(49, n, n--; binomial(49,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(49, n) for n in range(50)] # Zerinvary Lajos, May 21 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^49.
E.g.f.: 1F1(-49; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A017816 Binomial coefficients C(100,n).

Original entry on oeis.org

1, 100, 4950, 161700, 3921225, 75287520, 1192052400, 16007560800, 186087894300, 1902231808400, 17310309456440, 141629804643600, 1050421051106700, 7110542499799200, 44186942677323600, 253338471349988640, 1345860629046814650, 6650134872937201800

Offset: 0

N. J. A. Sloane

Row 100 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..100 (full sequence)

Cf. A010926-A011001, A017765-A017815.

seq(binomial(100,n), n=0..100); # Nathaniel Johnston, Jun 24 2011

Binomial[100,Range[0,20]] (* Harvey P. Dale, Jul 08 2016 *)

[binomial(100, n) for n in range(16)] # Zerinvary Lajos, May 29 2009

A010928 Binomial coefficient C(12,n).

Original entry on oeis.org

1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1

Offset: 0

N. J. A. Sloane

Row 12 of A007318.
Also number of positions that are exactly n moves from the starting position in the Orbix Type 1 puzzle. This is the number of positions that can be reached in n moves from the start, but which cannot be reached in fewer than n moves. A puzzle in the Rubik cube family. The total number of distinct positions is 4096. Here positions differing by rotations or reflections are considered distinct.
If the sequence is extended by trailing zeros, its binomial transform yields A010965. - R. J. Mathar, Sep 19 2008

Jaap Scherphuis, Puzzle Pages

Cf. A010926-A011001, A080560-A080564.

[Binomial(12, n): n in [0..12]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(12,n), n=0..12); # Nathaniel Johnston, Jun 23 2011

q = 12; Join[{a = 1}, Table[a = (q - n)*a/(n + 1), {n, 0, q - 1}]] (* Vladimir Joseph Stephan Orlovsky, Jul 09 2011 *)
Binomial[12,Range[0,12]] (* Harvey P. Dale, Jul 02 2018 *)

[binomial(12,m) for m in range(13)] # Zerinvary Lajos, Apr 21 2009

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007

A017768 Binomial coefficients C(52,n).

Original entry on oeis.org

1, 52, 1326, 22100, 270725, 2598960, 20358520, 133784560, 752538150, 3679075400, 15820024220, 60403728840, 206379406870, 635013559600, 1768966344600, 4481381406320, 10363194502115, 21945588357420, 42671977361650, 76360380541900, 125994627894135

Offset: 0

N. J. A. Sloane

Row 52 of A007318.

Nathaniel Johnston, Table of n, a(n) for n = 0..52 (full sequence)

Cf. A010926-A011001, A017765-A017816.

[Binomial(52,n): n in [0..52]]; // G. C. Greubel, Nov 13 2018

seq(binomial(52,n), n=0..52); # Nathaniel Johnston, Jun 24 2011

Binomial[52,Range[0,50]] (* Harvey P. Dale, Jun 02 2017 *)

vector(52, n, n--; binomial(52,n)) \\ G. C. Greubel, Nov 13 2018

[binomial(52, n) for n in range(53)] # Zerinvary Lajos, May 23 2009

From G. C. Greubel, Nov 13 2018: (Start)
G.f.: (1+x)^52.
E.g.f.: 1F1(-52; 1; -x), where 1F1 is the confluent hypergeometric function. (End)

A010940 Binomial coefficient C(24,n).

Original entry on oeis.org

1, 24, 276, 2024, 10626, 42504, 134596, 346104, 735471, 1307504, 1961256, 2496144, 2704156, 2496144, 1961256, 1307504, 735471, 346104, 134596, 42504, 10626, 2024, 276, 24, 1

Offset: 0

N. J. A. Sloane

Row 24 of A007318.

Cf. A010926-A011001.

[Binomial(24, n): n in [0..24]]; // Vincenzo Librandi, Jun 12 2013

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

q = 24; Join[{a = 1}, Table[a = (q - n)*a/(n + 1), {n, 0, q - 1}]] (* Vladimir Joseph Stephan Orlovsky, Jul 10 2011 *)
Binomial[24,Range[0,24]] (* Harvey P. Dale, Jun 03 2014 *)

[binomial(24,m) for m in range(25)] # Zerinvary Lajos, Apr 21 2009

A017770 Binomial coefficients C(54,n).

Original entry on oeis.org

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)

cp's OEIS Frontend

A017765 Binomial coefficients C(49,n).

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A017816 Binomial coefficients C(100,n).

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A010928 Binomial coefficient C(12,n).

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A017768 Binomial coefficients C(52,n).

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A010940 Binomial coefficient C(24,n).

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A017770 Binomial coefficients C(54,n).

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Magma

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Sage

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A017771 Binomial coefficients C(55,n).

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