A097805 -id:A097805 - cp's OEIS frontend

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

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

A170757 Expansion of g.f.: (1+x)/(1-37*x).

Original entry on oeis.org

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086, 342458329247810315388182

Offset: 0

N. J. A. Sloane, Dec 04 2009

G. C. Greubel, Table of n, a(n) for n = 0..634
Index entries for linear recurrences with constant coefficients, signature (37).

Cf. A003945.

k:=38;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 09 2019

k:=38; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 09 2019

k:=38; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 09 2019

With[{k = 38}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 09 2019 *)

vector(26, n, k=38; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 09 2019

k=38; [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)*38^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 38*37^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (1/37)*(38*exp(37*x) - 1). - Stefano Spezia, Oct 09 2019

A170759 Expansion of g.f.: (1+x)/(1-39*x).

Original entry on oeis.org

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664040, 12699033492898897560, 495262306223057004840, 19315229942699223188760, 753293967765269704361640

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 (39).

Cf. A003945.

k:=40;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

[1] cat [40*39^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012

k:=40; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-39*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 40}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

vector(26, n, k=40; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=40; [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)*40^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 40*39^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0)=1, a(1)=40, a(n) = 39*a(n-1). - Vincenzo Librandi, Dec 10 2012
E.g.f.: (40*exp(39*x) - 1)/39. - G. C. Greubel, Oct 10 2019

A170760 Expansion of g.f.: (1+x)/(1-40*x).

Original entry on oeis.org

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000, 1100585369600000000000000

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 (40).

Cf. A003945.

k:=41;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=41; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=41; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-40*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 41}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[40#&,41,20]] (* Harvey P. Dale, Jun 19 2023 *)

vector(26, n, k=41; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=41; [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)*41^k. - Philippe Deléham, Dec 04 2009
a(0)=1; for n>0, a(n) = 41*40^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0)=1, a(1)=41, a(n) = 40*a(n-1). - Vincenzo Librandi, Dec 10 2012
E.g.f.: (41*exp(40*x) - 1)/40. - G. C. Greubel, Oct 10 2019

A170761 Expansion of g.f.: (1+x)/(1-41*x).

Original entry on oeis.org

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082434522, 947666592615379815402, 38854330297230572431482, 1593027542186453469690762

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 (41).

Cf. A003945.

k:=42;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=42; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=42; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-41*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)
With[{k = 42}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[41#&,42,20]] (* Harvey P. Dale, Feb 02 2022 *)

vector(26, n, k=42; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=42; [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)*42^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 42*41^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0)=1, a(1)=42, a(n) = 41*a(n-1). - Vincenzo Librandi, Dec 10 2012
E.g.f.: (42*exp(41*x) - 1)/41. - G. C. Greubel, Oct 10 2019

A170763 Expansion of g.f.: (1+x)/(1-43*x).

Original entry on oeis.org

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506956, 40888924536733799108, 1758223755079553361644, 75603621468420794550692, 3250955723142094165679756

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 (43).

Cf. A003945.

k:=44;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

[1] cat [44*43^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 11 2012

k:=44; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-43*x), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 09 2012 *)
Join[{1},NestList[43#&,44,20]] (* Harvey P. Dale, Jan 15 2013 *)
With[{k = 44}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

a(n)=44*43^n\43 \\ Charles R Greathouse IV, Jul 01 2013

k=44; [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)*44^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 44*43^(n-1). - Vincenzo Librandi, Dec 05 2009
a(0)=1, a(1)=44, a(n) = 43*a(n-1). - Vincenzo Librandi, Dec 11 2012
E.g.f.: (44*exp(43*x) - 1)/43. - G. C. Greubel, Oct 10 2019

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

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

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

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

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

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A170757 Expansion of g.f.: (1+x)/(1-37*x).

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