A003945 -id:A003945 - cp's OEIS frontend

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

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

A170764 Expansion of g.f.: (1+x)/(1-44*x).

Original entry on oeis.org

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280, 4587224388472863530680320

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 (44).

Cf. A003945.

k:=45;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=45; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=45; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-44*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 45}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[44#&,45,20]] (* Harvey P. Dale, Aug 22 2021 *)

vector(26, n, k=45; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=45; [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)*45^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 45*44^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (45*exp(44*x) - 1)/44. - G. C. Greubel, Oct 10 2019

A170765 Expansion of g.f.: (1+x)/(1-45*x).

Original entry on oeis.org

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750, 6422927569141882324218750

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 (45).

Cf. A003945.

k:=46;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=46; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=46; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-45x),{x,0,15}],x]  (* Harvey P. Dale, Mar 26 2011 *)
With[{k = 46}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

a(n)=46*45^n\45 \\ Charles R Greathouse IV, Jun 16 2011

vector(26, n, k=46; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=46; [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)*46^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 46*45^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (46*exp(45*x) - 1)/45. - G. C. Greubel, Oct 10 2019

A170766 Expansion of g.f.: (1+x)/(1-46*x).

Original entry on oeis.org

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762957312, 4218828178657096036352, 194066096218226417672192, 8927040426038415212920832

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 (46).

Cf. A003945.

k:=47;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=47; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=47; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-46*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 47}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

vector(26, n, k=47; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=47; [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)*47^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 47*46^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (47*exp(46*x) - 1)/46. - G. C. Greubel, Oct 11 2019

A170767 Expansion of g.f.: (1+x)/(1-47*x).

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696, 12320015337008035648049712

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 (47).

Cf. A003945.

k:=48;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=48; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=48; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-47*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 48}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)
Join[{1},NestList[47#&,48,20]] (* Harvey P. Dale, Nov 07 2021 *)

vector(26, n, k=48; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=48; [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)*48^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 48*47^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (48*exp(47*x) - 1)/47. - G. C. Greubel, Oct 11 2019

A170768 Expansion of g.f.: (1+x)/(1-48*x).

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192, 16887812686401712963977216

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 (48).

Cf. A003945.

k:=49;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Oct 10 2019

k:=49; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Oct 10 2019

k:=49; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Oct 10 2019

CoefficientList[Series[(1+x)/(1-48*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2012 *)
With[{k = 49}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* G. C. Greubel, Oct 10 2019 *)

vector(26, n, k=49; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Oct 10 2019

k=49; [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)*49^k. - Philippe Deléham, Dec 04 2009
a(0) = 1; for n>0, a(n) = 49*48^(n-1). - Vincenzo Librandi, Dec 05 2009
E.g.f.: (49*exp(48*x) - 1)/48. - G. C. Greubel, Oct 11 2019

cp's OEIS Frontend

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

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

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

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

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

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A170764 Expansion of g.f.: (1+x)/(1-44*x).

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