A003945 -id:A003945 - cp's OEIS frontend

A170746 Expansion of g.f.: (1+x)/(1-26*x).

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352, 45286002241714599985152, 1177436058284579599613952

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..706
Index entries for linear recurrences with constant coefficients, signature (26).

Cf. A003945, A097805.

k:=27;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=27; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=27; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

CoefficientList[Series[(1+x)/(1-26x),{x,0,20}],x] (* or *) Join[ {1}, NestList[26#&,27,20]] (* Harvey P. Dale, Jun 16 2016 *)

vector(26, n, k=27; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,27*26**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=27; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*27^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 27*26^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (27*exp(26*x) - 1)/26. - G. C. Greubel, Sep 25 2019

A170747 Expansion of g.f.: (1+x)/(1-27*x).

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852, 82720755783423343562004, 2233460406152430276174108

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..698
Index entries for linear recurrences with constant coefficients, signature (27).

Cf. A003945, A097805.

k:=28;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=28; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=28; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

With[{k=28}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* G. C. Greubel, Sep 25 2019 *)

vector(26, n, k=28; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,28*27**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=28; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*28^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n > 0, a(n) = 28*27^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (28*exp(27*x) - 1)/27. - G. C. Greubel, Sep 25 2019

A170748 Expansion of g.f.: (1+x)/(1-28*x).

Original entry on oeis.org

1, 29, 812, 22736, 636608, 17825024, 499100672, 13974818816, 391294926848, 10956257951744, 306775222648832, 8589706234167296, 240511774556684288, 6734329687587160064, 188561231252440481792, 5279714475068333490176, 147832005301913337724928

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..690
Index entries for linear recurrences with constant coefficients, signature (28).

Cf. A003945, A097805.

k:=29;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=29; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=29; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Join[{1},Table[29*28^(n-1),{n,20}]] (* or *) Join[{1}, NestList[28#&, 29, 20]] (* Harvey P. Dale, Feb 05 2012 *)

vector(26, n, k=29; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,29*28**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=29; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*29^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 29*28^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (29*exp(28*x) -1)/28. - G. C. Greubel, Sep 25 2019

A170750 Expansion of g.f.: (1+x)/(1-30*x).

Original entry on oeis.org

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000, 444816117000000000000000

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..676
Index entries for linear recurrences with constant coefficients, signature (30).

Cf. A003945, A097805.

k:=31;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=31; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=31; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

CoefficientList[Series[(1+x)/(1-30x), {x, 0, 25}], x] (* Michael De Vlieger, Aug 04 2017 *)
With[{k = 31}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Sep 25 2019 *)
LinearRecurrence[{30},{1,31},20] (* Harvey P. Dale, Sep 25 2024 *)

vector(26, n, k=31; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,31*30**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=31; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 25 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*31^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 31*30^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (31*exp(30*x) - 1)/30. - G. C. Greubel, Sep 25 2019

A170751 Expansion of g.f.: (1+x)/(1-31*x).

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272, 750888383739029949758432

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..670
Index entries for linear recurrences with constant coefficients, signature (31).

Cf. A003945.

k:=32;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=32; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=32; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

With[{k = 32}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=32; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

for i in range(1001):print(i,32*31**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=32; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*32^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 32*31^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (1/31)*(32*exp(31*x) - 1). - Stefano Spezia, Oct 09 2019

A170752 Expansion of g.f.: (1+x)/(1-32*x).

Original entry on oeis.org

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992, 1246704751477586336415744

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..664
Index entries for linear recurrences with constant coefficients, signature (32).

Cf. A003945.

k:=33;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=33; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=33; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

With[{k = 33}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=33; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

for i in range(1001):print(i,33*32**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=33; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*33^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 33*32^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (1/32)*(33*exp(32*x) - 1) - Stefano Spezia, Oct 09 2019

A170753 Expansion of g.f.: (1+x)/(1-33*x).

Original entry on oeis.org

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469666402, 52073685498991266, 1718431621466711778, 56708243508401488674, 1871372035777249126242, 61755277180649221165986, 2037924146961424298477538

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..658
Index entries for linear recurrences with constant coefficients, signature (33).

Cf. A003945.

k:=34;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=34; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=34; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

With[{k = 34}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=34; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

for i in range(1001):print(i,34*33**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=34; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*34^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 34*33^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (1/33)*(34*exp(33*x) - 1). - Stefano Spezia, Oct 09 2019

A170754 Expansion of g.f.: (1+x)/(1-34*x).

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760, 3282855749315577536675840

Offset: 0

N. J. A. Sloane, Dec 04 2009

G. C. Greubel, Table of n, a(n) for n = 0..649
Index entries for linear recurrences with constant coefficients, signature (34).

Cf. A003945.

k:=35;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=35; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=35; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

CoefficientList[Series[(1+x)/(1-34x),{x,0,30}],x] (* Harvey P. Dale, Aug 23 2016 *)
With[{k = 35}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=35; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

k=35; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

a(n)= Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*35^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 35*34^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (1/34)*(35*exp(34*x) - 1). - Stefano Spezia, Oct 09 2019

A170755 Expansion of g.f.: (1+x)/(1-35*x).

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500

Offset: 0

N. J. A. Sloane, Dec 04 2009

G. C. Greubel, Table of n, a(n) for n = 0..644
Index entries for linear recurrences with constant coefficients, signature (35).

Cf. A003945.

k:=36;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=36; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=36; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

With[{k = 36}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=36; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

k=36; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*36^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 36*35^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (1/35)*(36*exp(35*x) - 1). - Stefano Spezia, Oct 09 2019

A170756 Expansion of g.f.: (1+x)/(1-36*x).

Original entry on oeis.org

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575872, 3757718396731392, 135277862282330112, 4870003042163884032, 175320109517899825152, 6311523942644393705472, 227214861935198173396992

Offset: 0

N. J. A. Sloane, Dec 04 2009

G. C. Greubel, Table of n, a(n) for n = 0..639
Index entries for linear recurrences with constant coefficients, signature (36).

Cf. A003945.

k:=37;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=37; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=37; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

With[{k = 37}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=37; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

k=37; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 09 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*37^k. - Philippe Deléham, Dec 04 2009

E.g.f.: (1/36)*(37*exp(36*x) - 1). - Stefano Spezia, Oct 09 2019

cp's OEIS Frontend

A170746 Expansion of g.f.: (1+x)/(1-26*x).

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A170747 Expansion of g.f.: (1+x)/(1-27*x).

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A170748 Expansion of g.f.: (1+x)/(1-28*x).

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A170750 Expansion of g.f.: (1+x)/(1-30*x).

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A170751 Expansion of g.f.: (1+x)/(1-31*x).

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A170752 Expansion of g.f.: (1+x)/(1-32*x).

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