A003945 -id:A003945 - cp's OEIS frontend

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

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

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

Original entry on oeis.org

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

cp's OEIS Frontend

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

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

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

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

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

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

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