A242091 -id:A242091 - cp's OEIS frontend

A010988 Binomial coefficient C(n,35).

1, 36, 666, 8436, 82251, 658008, 4496388, 26978328, 145008513, 708930508, 3190187286, 13340783196, 52251400851, 192928249296, 675248872536, 2250829575120, 7174519270695, 21945588357420, 64617565719070, 183649923622620, 505037289962205, 1346766106565880

Offset: 35

N. J. A. Sloane

nonn

T. D. Noe, Table of n, a(n) for n = 35..1000
Index entries for linear recurrences with constant coefficients, signature (36, -630, 7140, -58905, 376992, -1947792, 8347680, -30260340, 94143280, -254186856, 600805296, -1251677700, 2310789600, -3796297200, 5567902560, -7307872110, 8597496600, -9075135300, 8597496600, -7307872110, 5567902560, -3796297200, 2310789600, -1251677700, 600805296, -254186856, 94143280, -30260340, 8347680, -1947792, 376992, -58905, 7140, -630, 36, -1).

Cf. A010985, A010986, A010987, A001787, A242091.

[Binomial(n, 35): n in [35..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,35),n=35..55); # Zerinvary Lajos, Dec 19 2008

Table[Binomial[n,35],{n,35,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

G.f.: x^35/(1-x)^36. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017
From Amiram Eldar, Dec 12 2020: (Start)
Sum_{n>=35} 1/a(n) = 35/34.
Sum_{n>=35} (-1)^(n+1)/a(n) = A001787(35)*log(2) - A242091(35)/34! = 601295421440*log(2) - 429895798851992810179897/1031453949240 = 0.9736160133... (End)

A010990 Binomial coefficient C(n,37).

Original entry on oeis.org

1, 38, 741, 9880, 101270, 850668, 6096454, 38320568, 215553195, 1101716330, 5178066751, 22595200368, 92263734836, 354860518600, 1292706174900, 4481381406320, 14844575908435, 47153358767970, 144079707346575, 424655979547800, 1210269541711230, 3342649210440540

Offset: 37

N. J. A. Sloane

nonn

T. D. Noe, Table of n, a(n) for n = 37..1000
Index entries for linear recurrences with constant coefficients, signature (38, -703, 8436, -73815, 501942, -2760681, 12620256, -48903492, 163011640, -472733756, 1203322288, -2707475148, 5414950296, -9669554100, 15471286560, -22239974430, 28781143380, -33578000610, 35345263800, -33578000610, 28781143380, -22239974430, 15471286560, -9669554100, 5414950296, -2707475148, 1203322288, -472733756, 163011640, -48903492, 12620256, -2760681, 501942, -73815, 8436, -703, 38, -1).

Cf. A010987, A010988, A010989, A001787, A242091.

[Binomial(n, 37): n in [37..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,37),n=37..55); # Zerinvary Lajos, Dec 19 2008

Table[Binomial[n,37],{n,37,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

G.f.: x^37/(1-x)^38. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=37} 1/a(n) = 37/36.
Sum_{n>=37} (-1)^(n+1)/a(n) = A001787(37)*log(2) - A242091(37)/36! = 2542620639232*log(2) - 31812289115104183594771283/18050444111700 = 0.9749413644... (End)

A017763 a(n) = binomial coefficient C(n,99).

Original entry on oeis.org

1, 100, 5050, 171700, 4421275, 91962520, 1609344100, 24370067800, 325949656825, 3911395881900, 42634215112710, 426342151127100, 3943664897925675, 33976189889821200, 274236389824985400

Offset: 99

N. J. A. Sloane

G. C. Greubel, Table of n, a(n) for n = 99..10000

Cf. A001787, A242091.

[Binomial(n,99): n in [99..120]]; // G. C. Greubel, Nov 12 2018

Table[Binomial[n,99],{n,99,5!}] (* Vladimir Joseph Stephan Orlovsky, Dec 25 2008 *)

a(n)=binomial(n,99) \\ Charles R Greathouse IV, Jun 28 2012

[binomial(n, 99) for n in range(99,114)] # Zerinvary Lajos, May 23 2009

From G. C. Greubel, Nov 12 2018: (Start)
G.f.: x^99/(1-x)^100.
E.g.f.: x^99*exp(x)/99!. (End)
From Amiram Eldar, Dec 20 2020: (Start)
Sum_{n>=99} 1/a(n) = 99/98.
Sum_{n>=99} (-1)^(n+1)/a(n) = A001787(99)*log(2) - A242091(99)/98! = 31374352355648677687043404333056*log(2) - 1914409165727592211172313915606888772651389180584205416988817447627229 / 88030776805192521672391172898121595400 = 0.9901924115... (End)

A010981 Binomial coefficient C(n,28).

Original entry on oeis.org

1, 29, 435, 4495, 35960, 237336, 1344904, 6724520, 30260340, 124403620, 472733756, 1676056044, 5586853480, 17620076360, 52860229080, 151532656696, 416714805914, 1103068603890, 2818953098830, 6973199770790, 16735679449896, 39049918716424, 88749815264600

Offset: 28

N. J. A. Sloane

Coordination sequence for 28-dimensional cyclotomic lattice Z[zeta_29].

T. D. Noe, Table of n, a(n) for n = 28..1000
Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
Index entries for linear recurrences with constant coefficients, signature (29, -406, 3654, -23751, 118755, -475020, 1560780, -4292145, 10015005, -20030010, 34597290, -51895935, 67863915, -77558760, 77558760, -67863915, 51895935, -34597290, 20030010, -10015005, 4292145, -1560780, 475020, -118755, 23751, -3654, 406, -29, 1).

Cf. A010980, A001787, A242091.

[Binomial(n, 28): n in [28..60]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,28),n=28..53); # Zerinvary Lajos, Aug 18 2008

Table[Binomial[n,28],{n,28,60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

x='x+O('x^50); Vec(x^28/(1-x)^29) \\ G. C. Greubel, Nov 23 2017

G.f.: x^28/(1-x)^29. - Zerinvary Lajos, Aug 18 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017
From Amiram Eldar, Dec 12 2020: (Start)
Sum_{n>=28} 1/a(n) = 28/27.
Sum_{n>=28} (-1)^n/a(n) = A001787(28)*log(2) - A242091(28)/27! = 3758096384*log(2) - 1867942673688249668/717084225 = 0.9676178392... (End)

A010982 Binomial coefficient C(n,29).

Original entry on oeis.org

1, 30, 465, 4960, 40920, 278256, 1623160, 8347680, 38608020, 163011640, 635745396, 2311801440, 7898654920, 25518731280, 78378960360, 229911617056, 646626422970, 1749695026860, 4568648125690, 11541847896480, 28277527346376, 67327446062800, 156077261327400

Offset: 29

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 29..1000
Index entries for linear recurrences with constant coefficients, signature (30, -435, 4060, -27405, 142506, -593775, 2035800, -5852925, 14307150, -30045015, 54627300, -86493225, 119759850, -145422675, 155117520, -145422675, 119759850, -86493225, 54627300, -30045015, 14307150, -5852925, 2035800, -593775, 142506, -27405, 4060, -435, 30, -1).

Cf. A010980, A010981, A001787, A242091.

[Binomial(n, 29): n in [29..60]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,29),n=29..53); # Zerinvary Lajos, Dec 19 2008

Table[Binomial[n,29],{n,29,60}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

x='x+O('x^50); Vec(x^29/(1-x)^30) \\ G. C. Greubel, Nov 23 2017

G.f.: x^29/(1-x)^30. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 21 2017
From Amiram Eldar, Dec 12 2020: (Start)
Sum_{n>=29} 1/a(n) = 29/28.
Sum_{n>=29} (-1)^(n+1)/a(n) = A001787(29)*log(2) - A242091(29)/28! = 7784628224*log(2) - 108340675094713923269/20078358300 = 0.9686369528... (End)

A010989 Binomial coefficient C(n,36).

Original entry on oeis.org

1, 37, 703, 9139, 91390, 749398, 5245786, 32224114, 177232627, 886163135, 4076350421, 17417133617, 69668534468, 262596783764, 937845656300, 3188675231420, 10363194502115, 32308782859535, 96926348578605, 280576272201225, 785613562163430, 2132379668729310

Offset: 36

N. J. A. Sloane

nonn

Coordination sequence for 36-dimensional cyclotomic lattice Z[zeta_37].

T. D. Noe, Table of n, a(n) for n = 36..1000
Matthias Beck and Serkan Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv:math/0508136 [math.CO], 2005-2006.
Index entries for linear recurrences with constant coefficients, signature (37, -666, 7770, -66045, 435897, -2324784, 10295472, -38608020, 124403620, -348330136, 854992152, -1852482996, 3562467300, -6107086800, 9364199760, -12875774670, 15905368710, -17672631900, 17672631900, -15905368710, 12875774670, -9364199760, 6107086800, -3562467300, 1852482996, -854992152, 348330136, -124403620, 38608020, -10295472, 2324784, -435897, 66045, -7770, 666, -37, 1).

Cf. A010986, A010987, A010988, A001787, A242091.

[Binomial(n, 36): n in [36..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,36),n=36..55); # Zerinvary Lajos, Dec 19 2008

Table[Binomial[n,36],{n,36,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

G.f.: x^36/(1-x)^37. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017
From Amiram Eldar, Dec 12 2020: (Start)
Sum_{n>=36} 1/a(n) = 36/35.
Sum_{n>=36} (-1)^n/a(n) = A001787(36)*log(2) - A242091(36)/35! = 1236950581248*log(2) - 429895798852508537154517/501401225325 = 0.9742957989... (End)

A010991 Binomial coefficient C(n,38).

Original entry on oeis.org

1, 39, 780, 10660, 111930, 962598, 7059052, 45379620, 260932815, 1362649145, 6540715896, 29135916264, 121399651100, 476260169700, 1768966344600, 6250347750920, 21094923659355, 68248282427325, 212327989773900, 636983969321700, 1847253511032930, 5189902721473470

Offset: 38

N. J. A. Sloane

nonn

T. D. Noe, Table of n, a(n) for n = 38..1000
Index entries for linear recurrences with constant coefficients, signature (39, -741, 9139, -82251, 575757, -3262623, 15380937, -61523748, 211915132, -635745396, 1676056044, -3910797436, 8122425444, -15084504396, 25140840660, -37711260990, 51021117810, -62359143990, 68923264410, -68923264410, 62359143990, -51021117810, 37711260990, -25140840660, 15084504396, -8122425444, 3910797436, -1676056044, 635745396, -211915132, 61523748, -15380937, 3262623, -575757, 82251, -9139, 741, -39, 1).

Cf. A010988, A010989, A010990, A001787, A242091.

[Binomial(n, 38): n in [38..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,38),n=38..57); # Zerinvary Lajos, Dec 19 2008

Table[Binomial[n,38],{n,38,66}] (* Vladimir Joseph Stephan Orlovsky, Apr 26 2011 *)

G.f.: x^38/(1-x)^39. - Zerinvary Lajos, Dec 19 2008; adapted to offset by Enxhell Luzhnica, Jan 23 2017
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=38} 1/a(n) = 38/37.
Sum_{n>=38} (-1)^n/a(n) = A001787(38)*log(2) - A242091(38)/37! = 5222680231936*log(2) - 31812289115113208816827133/8787716212275 = 0.9755552351... (End)

A010992 Binomial coefficient C(n,39).

Original entry on oeis.org

1, 40, 820, 11480, 123410, 1086008, 8145060, 53524680, 314457495, 1677106640, 8217822536, 37353738800, 158753389900, 635013559600, 2403979904200, 8654327655120, 29749251314475, 97997533741800, 310325523515700, 947309492837400, 2794563003870330

Offset: 39

N. J. A. Sloane

nonn

T. D. Noe, Table of n, a(n) for n = 39..1000
Index entries for linear recurrences with constant coefficients, signature (40, -780, 9880, -91390, 658008, -3838380, 18643560, -76904685, 273438880, -847660528, 2311801440, -5586853480, 12033222880, -23206929840, 40225345056, -62852101650, 88732378800, -113380261800, 131282408400, -137846528820, 131282408400, -113380261800, 88732378800, -62852101650, 40225345056, -23206929840, 12033222880, -5586853480, 2311801440, -847660528, 273438880, -76904685, 18643560, -3838380, 658008, -91390, 9880, -780, 40, -1).

Cf. A010990, A010991, A001787, A242091.

[Binomial(n, 39): n in [39..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,39),n=39..57); # Zerinvary Lajos, Dec 19 2008

Table[Binomial[n,39],{n,39,70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

G.f.: x^39/(1-x)^40. - Zerinvary Lajos, Dec 19 2008
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=39} 1/a(n) = 39/38.
Sum_{n>=39} (-1)^(n+1)/a(n) = A001787(39)*log(2) - A242091(39)/38! = 10720238370816*log(2) - 63624578230235205349866541/8562390155550 = 0.9761396932... (End)

A010994 a(n) = binomial coefficient C(n,41).

Original entry on oeis.org

1, 42, 903, 13244, 148995, 1370754, 10737573, 73629072, 450978066, 2505433700, 12777711870, 60403728840, 266783135710, 1108176102180, 4353548972850, 16253249498640, 57902201338905, 197548686920970, 647520696018735, 2044802197953900, 6236646703759395

Offset: 41

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 41..1000
Index entries for linear recurrences with constant coefficients, signature (42, -861, 11480, -111930, 850668, -5245786, 26978328, -118030185, 445891810, -1471442973, 4280561376, -11058116888, 25518731280, -52860229080, 98672427616, -166509721602, 254661927156, -353697121050, 446775310800, -513791607420, 538257874440, -513791607420, 446775310800, -353697121050, 254661927156, -166509721602, 98672427616, -52860229080, 25518731280, -11058116888, 4280561376, -1471442973, 445891810, -118030185, 26978328, -5245786, 850668, -111930, 11480, -861, 42, -1).

Cf. A010990, A010991, A010992, A001787, A242091.

[Binomial(n, 41): n in [41..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,41),n=41..57); # Zerinvary Lajos, Dec 20 2008

Table[Binomial[n,41],{n,41,70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

G.f.: x^41/(1-x)^42. - Zerinvary Lajos, Dec 20 2008
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=41} 1/a(n) = 41/40.
Sum_{n>=41} (-1)^(n+1)/a(n) = A001787(41)*log(2) - A242091(41)/40! = 45079976738816*log(2) - 41737723319038472299669343741/1335732864265800 = 0.9772284535... (End)

A010996 Binomial coefficient C(n,43).

Original entry on oeis.org

1, 44, 990, 15180, 178365, 1712304, 13983816, 99884400, 636763050, 3679075400, 19499099620, 95722852680, 438729741450, 1889912732400, 7694644696200, 29752626158640, 109712808959985, 387221678682300, 1312251244423350, 4282083008118300, 13488561475572645

Offset: 43

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 43..1000
Index entries for linear recurrences with constant coefficients, signature (44, -946, 13244, -135751, 1086008, -7059052, 38320568, -177232627, 708930508, -2481256778, 7669339132, -21090682613, 51915526432, -114955808528, 229911617056, -416714805914, 686353797976, -1029530696964, 1408831480056, -1761039350070, 2012616400080, -2104098963720, 2012616400080, -1761039350070, 1408831480056, -1029530696964, 686353797976, -416714805914, 229911617056, -114955808528, 51915526432, -21090682613, 7669339132, -2481256778, 708930508, -177232627, 38320568, -7059052, 1086008, -135751, 13244, -946, 44, -1).

Cf. A010994, A010996, A001787, A242091.

[Binomial(n, 43): n in [43..70]]; // Vincenzo Librandi, Jun 12 2013

seq(binomial(n,43),n=43..57); # Zerinvary Lajos, Dec 20 2008

Table[Binomial[n, 43], {n, 43, 70}] (* Vladimir Joseph Stephan Orlovsky, May 16 2011 *)

G.f.: x^43/(1-x)^44. - Zerinvary Lajos, Dec 20 2008
From Amiram Eldar, Dec 15 2020: (Start)
Sum_{n>=43} 1/a(n) = 43/42.
Sum_{n>=43} (-1)^(n+1)/a(n) = A001787(43)*log(2) - A242091(43)/42! = 189115999977472*log(2) - 897361051359348522193323713869/6845630929362225 = 0.9782220374... (End)

cp's OEIS Frontend

A010988 Binomial coefficient C(n,35).

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A010990 Binomial coefficient C(n,37).

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A017763 a(n) = binomial coefficient C(n,99).

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A010981 Binomial coefficient C(n,28).

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A010982 Binomial coefficient C(n,29).

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A010989 Binomial coefficient C(n,36).

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A010991 Binomial coefficient C(n,38).

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