A097805 -id:A097805 - cp's OEIS frontend

A170749 Expansion of g.f.: (1+x)/(1-29*x).

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430, 258875662427945533228470

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..683
Index entries for linear recurrences with constant coefficients, signature (29).

Cf. A003945, A097805.

k:=30;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 25 2019

k:=30; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 25 2019

k:=30; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 25 2019

With[{k=30}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* G. C. Greubel, Sep 25 2019 *)
Join[{1},NestList[29#&,30,20]] (* Harvey P. Dale, Aug 27 2020 *)

vector(26, n, k=30; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 25 2019

for i in range(31):print(i,30*29**(i-1) if i>0 else 1) # Kenny Lau, Aug 03 2017

k=30; [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)*30^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n > 0, a(n) = 30*29^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (30*exp(29*x) -1)/29. - G. C. Greubel, Sep 25 2019

A170762 Expansion of g.f.: (1+x)/(1-42*x).

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016, 2285380519500593123868672

Offset: 0

N. J. A. Sloane, Dec 04 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (42).

Cf. A003945.

k:=43;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=43; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=43; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-42x),{x,0,30}],x] (* or *) Join[{1}, NestList[42#&,43,30]] (* Harvey P. Dale, Mar 26 2012 *)
With[{k = 43}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

a(n)=if(n,43*42^(n-1),1) \\ Charles R Greathouse IV, Mar 22 2016

k=43; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*43^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 43*42^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0)=1, a(1)=43, a(n)=42*a(n-1). - Harvey P. Dale, Mar 26 2012
E.g.f.: (43*exp(42*x) - 1)/42. - G. C. Greubel, Oct 10 2019

A170769 Expansion of g.f.: (1+x)/(1-49*x).

Original entry on oeis.org

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895522450, 3989613314880600050, 195491052429149402450, 9579061569028320720050, 469374016882387715282450, 22999326827236998048840050

Offset: 0

N. J. A. Sloane, Dec 04 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (49).

Cf. A003945.

k:=50;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=50; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=50; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-49*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 50}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

A170769(n):=if n=0 then 1 else 50*49^(n-1)$
makelist(A170769(n),n,0,30); /* Martin Ettl, Nov 06 2012 */

vector(26, n, k=50; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=50; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Oct 10 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*50^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 50*49^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (50*exp(49*x) - 1)/49. - G. C. Greubel, Oct 11 2019

A170734 Expansion of g.f.: (1+x)/(1-14*x).

Original entry on oeis.org

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183360, 32669300067140567040, 457370200939967938560, 6403182813159551139840

Offset: 0

N. J. A. Sloane, Dec 04 2009

For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,14} with no two adjacent letters identical. -Milan Janjic, Jan 31 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..800
M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, J. Int. Seq. 18 (2015) # 15.4.7.
Index entries for linear recurrences with constant coefficients, signature (14).

Cf. A003945, A003954, A097805, A170733.

k:=15;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

k:=15; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

k:=15; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Join[{1}, 15*14^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-14x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)

vector(26, n, k=15; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

k=15; [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)*15^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 15*14^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0) = 1, a(1) = 15, a(n) = 14*a(n-1). - Vincenzo Librandi, Dec 10 2012
E.g.f.: (15*exp(14*x) -1)/14. - G. C. Greubel, Sep 24 2019

A170735 Expansion of g.f.: (1+x)/(1-15*x).

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000, 105094533691406250000, 1576418005371093750000, 23646270080566406250000

Offset: 0

N. J. A. Sloane, Dec 04 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..800
Index entries for linear recurrences with constant coefficients, signature (15).

Concatenation([1], List([1..20], n-> 16*15^(n-1) )); # G. C. Greubel, Sep 23 2019

[1] cat[16*15^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 10 2012

seq(`if`(n=0, 1, 16*15^(n-1)), n=0..20); # G. C. Greubel, Sep 23 2019

Join[{1},16*15^Range[0,25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-15x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
Join[{1},NestList[15#&,16,20]] (* Harvey P. Dale, Sep 25 2015 *)

vector(20, n, if(n==1, 1, 16*15^(n-2))) \\ G. C. Greubel, Sep 23 2019

[1]+[16*15^(n-1) for n in (1..20)] # G. C. Greubel, Sep 23 2019

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*16^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 16*15^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0)=1, a(1)=16, a(n) = 15*a(n-1). - Vincenzo Librandi, Dec 10 2012
E.g.f.: (16*exp(15*x) - 1)/15. - G. C. Greubel, Sep 23 2019

A170736 Expansion of g.f.: (1+x)/(1-16*x).

Original entry on oeis.org

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162755072, 4785074604081152, 76561193665298432, 1224979098644774912, 19599665578316398592, 313594649253062377472, 5017514388048998039552

Offset: 0

N. J. A. Sloane, Dec 04 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..800
Index entries for linear recurrences with constant coefficients, signature (16).

Cf. A003945, A097805.

k:=17;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

[1] cat [17*16^(n-1): n in [1..25]]; // Vincenzo Librandi, Dec 11 2012

k:=17; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Join[{1},17*16^Range[0,25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-16*x), {x, 0, 25}], x] (* Vincenzo Librandi, Dec 11 2012 *)

vector(26, n, k=17; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

k=17; [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)*17^k. - Philippe Deléham, Dec 04 2009
a(n) = 17*16^(n-1). - Vincenzo Librandi, Dec 11 2012
a(0)=1, a(1)=17, a(n) = 16*a(n-1). - Vincenzo Librandi, Dec 11 2012
E.g.f.: (17*exp(16*x) - 1)/16. - G. C. Greubel, Sep 24 2019

A170737 Expansion of g.f.: (1+x)/(1-17*x).

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274, 875901453762003632658, 14890324713954061755186

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..812
Index entries for linear recurrences with constant coefficients, signature (17).

Cf. A003945, A097805.

k:=18;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

k:=18; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

k:=18; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Join[{1},18*17^Range[0,25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-17x),{x,0,30}],x] (* or *) LinearRecurrence[ {17},{1,18},30] (* or *) Join[{1},NestList[ 17#&,18,30]] (* Harvey P. Dale, Jul 11 2015 *)

a(n)=18*17^n\17 \\ Charles R Greathouse IV, Jul 11 2016

for i in range(31):print(i,18*17**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

k=18; [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)*18^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 18*17^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (18*exp(17*x) -1)/17. - G. C. Greubel, Sep 24 2019

A170738 Expansion of g.f.: (1+x)/(1-18*x).

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752192, 7121453984059539456, 128186171713071710208, 2307351090835290783744, 41532319635035234107392

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..796
Index entries for linear recurrences with constant coefficients, signature (18).

Cf. A003945, A097805.

k:=19;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

k:=19; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

k:=19; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Join[{1},19*18^Range[0,25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-18x),{x,0,20}],x] (* or *) LinearRecurrence[ {18},{1,19},20] (* Harvey P. Dale, Jul 01 2017 *)

vector(26, n, k=19; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

for i in range(31):print(i,19*18**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

k=19; [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)*19^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 19*18^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (19*exp(18*x) -1)/18. - G. C. Greubel, Sep 24 2019

A170739 Expansion of g.f.: (1+x)/(1-19*x).

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420, 303622540597495965980, 5768828271352423353620, 109607737155696043718780

Offset: 0

N. J. A. Sloane, Dec 04 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (19).

Cf. A003945, A097805.

k:=20;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

[1] cat [20*19^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 05 2012

k:=20; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Join[{1}, 20*19^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-19x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 05 2012 *)
Join[{1},NestList[19#&,20,20]] (* Harvey P. Dale, Nov 26 2022 *)

a(n)=20*19^n\19 \\ Charles R Greathouse IV, Jul 01 2013

k=20; [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)*20^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 20*19^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0) = 1, a(1) = 20; for n>1, a(n) = 19*a(n-1). - Vincenzo Librandi, Dec 05 2012
E.g.f.: (20*exp(19*x) - 1)/19. - G. C. Greubel, Sep 24 2019

A170740 Expansion of g.f.: (1+x)/(1-20*x).

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000, 688128000000000000000, 13762560000000000000000, 275251200000000000000000

Offset: 0

N. J. A. Sloane, Dec 04 2009

Kenny Lau, Table of n, a(n) for n = 0..768
Index entries for linear recurrences with constant coefficients, signature (20).

Cf. A003945, A097805.

k:=21;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

k:=21; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019

k:=21; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Join[{1}, 21*20^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)

vector(26, n, k=21; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019

for i in range(31):print(i,21*20**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017

k=21; [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)*21^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 21*20^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f: (21*exp(20*x) - 1)/20. - G. C. Greubel, Sep 24 2019

cp's OEIS Frontend

A170749 Expansion of g.f.: (1+x)/(1-29*x).

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A170762 Expansion of g.f.: (1+x)/(1-42*x).

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A170769 Expansion of g.f.: (1+x)/(1-49*x).

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A170734 Expansion of g.f.: (1+x)/(1-14*x).

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A170735 Expansion of g.f.: (1+x)/(1-15*x).

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A170736 Expansion of g.f.: (1+x)/(1-16*x).

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