A097805 -id:A097805 - cp's OEIS frontend

A170741 Expansion of g.f.: (1+x)/(1-21*x).

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982, 1498691008824937010622, 31472511185323677223062, 660922734891797221684302

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..756
Index entries for linear recurrences with constant coefficients, signature (21).

Cf. A003945.

k:=22;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=22; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=22; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

Join[{1}, 22*21^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
Join[{1},NestList[21#&,22,20]] (* Harvey P. Dale, Jul 29 2018 *)

vector(26, n, k=22; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,22*21**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

k=22; [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)*22^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 22*21^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (22*exp(21*x) - 1)/21. - G. C. Greubel, Sep 25 2019

A170742 Expansion of g.f.: (1+x)/(1-22*x).

Original entry on oeis.org

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512, 3148241564354477195264, 69261314415798498295808, 1523748917147566962507776

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..744
Index entries for linear recurrences with constant coefficients, signature (22).

Cf. A003945, A097805.

k:=23;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=23; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=23; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

With[{k=23}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* G. C. Greubel, Sep 25 2019 *)
LinearRecurrence[{22},{1,23},20] (* Harvey P. Dale, Oct 13 2022 *)

vector(26, n, k=23; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,23*22**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

k=23; [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)*23^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 23*22^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (23*exp(22*x) - 1)/22. - G. C. Greubel, Sep 25 2019

A170743 Expansion of g.f.: (1+x)/(1-23*x).

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416, 6399245651145389894568, 147182649976343967575064

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..733
Index entries for linear recurrences with constant coefficients, signature (23).

Cf. A003945, A097805.

k:=24;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=24; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=24; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

CoefficientList[Series[(1+x)/(1-23x),{x,0,20}],x] (* or *) LinearRecurrence[ {23},{1,24},20] (* or *) Join[{1},NestList[ 23#&,24,20]] (* Harvey P. Dale, Oct 21 2015 *)

Vec((1+x)/(1-23*x) + O(x^18)) \\ Felix Fröhlich, Aug 02 2017

for i in range(1001):print(i,24*23**(i-1) if i>0 else 1) # Kenny Lau, Aug 02 2017

k=24; [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)*24^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 24*23^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (24*exp(23*x) -1)/23. - G. C. Greubel, Sep 25 2019

A170744 Expansion of g.f.: (1+x)/(1-24*x).

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400, 12621432073901152665600, 302914369773627663974400

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..724
Index entries for linear recurrences with constant coefficients, signature (24).

Cf. A003945, A097805.

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

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

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

Join[{1},NestList[24#&,25,30]] (* Harvey P. Dale, Jan 19 2019 *)

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

for i in range(31):print(i,25*24**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=25; [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)*25^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 25*24^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (25*exp(24*x) - 1)/24. - G. C. Greubel, Sep 25 2019

A170745 Expansion of g.f.: (1+x)/(1-25*x).

Original entry on oeis.org

1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566406250, 1549720764160156250, 38743019104003906250, 968575477600097656250, 24214386940002441406250, 605359673500061035156250

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..715
Index entries for linear recurrences with constant coefficients, signature (25).

Cf. A003945, A097805.

k:=26;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=26; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=26; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

CoefficientList[Series[(1+x)/(1-25*x),{x,0,20}],x] (* or *) Join[ {1}, NestList[25#&,26,20]] (* Harvey P. Dale, Aug 08 2019 *)

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

for i in range(31):print(i,26*25**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=26; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

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

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

Original entry on oeis.org

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

cp's OEIS Frontend

A170741 Expansion of g.f.: (1+x)/(1-21*x).

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A170742 Expansion of g.f.: (1+x)/(1-22*x).

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A170743 Expansion of g.f.: (1+x)/(1-23*x).

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A170744 Expansion of g.f.: (1+x)/(1-24*x).

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A170745 Expansion of g.f.: (1+x)/(1-25*x).

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

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