A128796 -id:A128796 - cp's OEIS frontend

A121607 (n^3+n)*3^n.

6, 90, 810, 5508, 31590, 161838, 765450, 3411720, 14526054, 59639490, 237731274, 924707340, 3523453830, 13191428502, 48642794730, 177008116752, 636661003590, 2266409860650, 7994034370026, 27964010896020, 97092998430246

Offset: 1

Mohammad K. Azarian, May 02 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A128796, A128960, A128985, A129002.

[(n^3 + n)*3^n: n in [1..30]]; // Vincenzo Librandi, Feb 22 2013

Table[(n^3 + n)*3^n, {n, 30}] (* or *) CoefficientList[Series[6 (1 + 3 x + 9 x^2)/(1 - 3 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

G.f.: 6*x*(1 + 3*x + 9*x^2)/(1 - 3*x)^4. - Vincenzo Librandi, Feb 22 2013

A127369 (n^3+n)*4^n.

Original entry on oeis.org

8, 160, 1920, 17408, 133120, 909312, 5734400, 34078720, 193462272, 1059061760, 5628755968, 29192355840, 148310589440, 740344987648, 3639984783360, 17660905521152, 84696755077120, 402008938905600, 1890610243960832

Offset: 1

Mohammad K. Azarian, May 02 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256).

Cf. A128796, A128960, A128985, A129002.

[(n^3 + n) * 4^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013

Table[(n^3 + n) 4^n, {n, 20}] (* Vincenzo Librandi Feb 22 2013 *)
LinearRecurrence[{16,-96,256,-256},{8,160,1920,17408},20] (* Harvey P. Dale, Aug 14 2021 *)

G.f.: 8*x*(1+4*x+16*x^2)/(1-4*x)^4. [R. J. Mathar, Dec 19 2008]

A128013 a(n) = (n^3 +n)*5^n.

Original entry on oeis.org

10, 250, 3750, 42500, 406250, 3468750, 27343750, 203125000, 1441406250, 9863281250, 65527343750, 424804687500, 2697753906250, 16833496093750, 103454589843750, 627441406250000, 3761291503906250, 22315979003906250

Offset: 1

Mohammad K. Azarian, May 02 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (20,-150,500,-625).

Cf. A128796, A128960, A128985, A129002.

[(n^3 + n)*5^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013

I:=[10,250,3750,42500]; [n le 4 select I[n] else 20*Self(n-1)-150*Self(n-2)+500*Self(n-3)-625*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013

Table[(n^3 + n) 5^n, {n, 30}] (* or *) CoefficientList[Series[10 (1 + 5 x + 25 x^2)/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

for(n=1, 30, print1((n^3 +n)*5^n, ", ")) \\ G. C. Greubel, May 08 2018

G.f.: 10*x(1+5*x+25*x^2)/(1-5*x)^4. - Vincenzo Librandi, Feb 22 2013

a(n) = 20*a(n-1) -150*a(n-2) +500*a(n-3) -625*a(n-4). - Vincenzo Librandi, Feb 23 2013

A128043 (n^3+n)*6^n.

Original entry on oeis.org

12, 360, 6480, 88128, 1010880, 10357632, 97977600, 873400320, 7437339648, 61070837760, 486873649152, 3787601264640, 28864133775360, 216128364576768, 1593927097712640, 11600403939459072, 83448431062548480

Offset: 1

Mohammad K. Azarian, May 02 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A128796, A128960, A128985, A129002.

[(n^3 + n)*6^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013

Table[(n^3 + n) * 6^n, {n, 30}] (* or *) CoefficientList[Series[12 (1 + 6 x + 36 x^2)/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

G.f.: 12*x*(1 + 6*x + 36*x^2)/(1 - 6*x)^4. - Vincenzo Librandi, Feb 22 2013

A128048 (n^3+n)*8^n.

Original entry on oeis.org

16, 640, 15360, 278528, 4259840, 58195968, 734003200, 8724152320, 99052683264, 1084479242240, 11527692222464, 119571889520640, 1214960348692480, 12129812277624832, 119275021381140480, 1157425104234217472

Offset: 1

Mohammad K. Azarian, May 02 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (32,-384,2048,-4096).

Cf. A128796, A128960, A128985, A129002.

[(n^3 + n)*8^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013

I:=[16,640,15360,278528]; [n le 4 select I[n] else 32*Self(n-1)-384*Self(n-2)+2048*Self(n-3)-4096*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013

Table[(n^3 + n) 8^n, {n, 30}] (* or *) CoefficientList[Series[16 (1 + 8 x + 64 x^2)/(1 - 8 x)^4, {x, 0, 20}],x] (* Vincenzo Librandi, Feb 22 2013 *)

G.f.: 16*x*(1+8*x+64*x^2)/(1-8*x)^4. - Vincenzo Librandi, Feb 22 2013

a(n) = 32*a(n-1) -384*a(n-2) +2048*a(n-3) -4096*a(n-4). - Vincenzo Librandi, Feb 23 2013

A128051 (n^3+n)*7^n.

Original entry on oeis.org

14, 490, 10290, 163268, 2184910, 26118078, 288240050, 2997696520, 29780961966, 285300001490, 2653572489106, 24083839729740, 214124712999470, 1870539234917542, 16094233518706770, 136653810502199312

Offset: 1

Mohammad K. Azarian, May 02 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A128796, A128960, A128985, A129002.

[(n^3 + n)*7^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013

Table[(n^3 + n) * 7^n, {n, 30}] (* or *) CoefficientList[Series[14 (1 + 7 x + 49 x^2)/(1 - 7 x)^4, {x, 0, 20}], x] (* Vincenzo Librandi, Feb 22 2013 *)

G.f.: 14*x*(1 + 7*x + 49*x^2)/(1 - 7*x)^4. - Vincenzo Librandi, Feb 22 2013

A128986 a(n) = (n^3 - n^2)*3^n.

Original entry on oeis.org

0, 36, 486, 3888, 24300, 131220, 642978, 2939328, 12754584, 53144100, 214347870, 841802544, 3233287044, 12187005012, 45199057050, 165299408640, 597144113712, 2133912053412, 7552375012566, 26499561447600, 92260315250460

Offset: 1

Mohammad K. Azarian, Apr 30 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Cf. A128796, A036289.

[(n^3 - n^2)*3^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

LinearRecurrence[{12, -54, 108, -81}, {0, 36, 486, 3888}, 30] (* Vincenzo Librandi, Feb 11 2013 *)

G.f.: 18x^2(2+3x)/(1-3x)^4. - R. J. Mathar, Dec 19 2008

a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 81*a(n-4). - Vincenzo Librandi, Feb 11 2013

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128987 a(n) = (n^3 - n^2)*4^n.

Original entry on oeis.org

0, 64, 1152, 12288, 102400, 737280, 4816896, 29360128, 169869312, 943718400, 5075107840, 26575110144, 136096776192, 683973541888, 3382286745600, 16492674416640, 79439715106816, 378506877861888, 1786156639322112

Offset: 1

Mohammad K. Azarian, Apr 30 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256).

Cf. A128796, A036289.

[(n^3 - n^2)*4^n: n in [1..25]]; // Vincenzo Librandi, Feb 11 2013

LinearRecurrence[{16, -96, 256, -256}, {0, 64, 1152, 12288}, 30] (* Vincenzo Librandi, Feb 11 2013 *)

G.f.: 64x^2(1+2x)/(1-4x)^4. - R. J. Mathar, Dec 19 2008

a(n) = 16*a(n-1) -96*a(n-2) +256*a(n-3)-256*a(n-4). - Vincenzo Librandi, Feb 11 2013

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128989 a(n) = (n^3 - n^2)*6^n.

Original entry on oeis.org

0, 144, 3888, 62208, 777600, 8398080, 82301184, 752467968, 6530347008, 54419558400, 438984437760, 3448023220224, 26487087464448, 199671890116608, 1481082701414400, 10833062044631040, 78268873272459264, 559392241329635328, 3959619590588203008, 27786804144478617600

Offset: 1

Mohammad K. Azarian, Apr 30 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (24,-216,864,-1296).

Cf. A128796, A036289.

[(n^3-n^2)*6^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

I:=[0,144,3888,62208]; [n le 4 select I[n] else 24*Self(n-1)-216*Self(n-2)+864*Self(n-3)-1296*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

CoefficientList[Series[144 x (1 + 3 x)/(1 - 6 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)
Table[(n^3-n^2)6^n,{n,20}] (* or *) LinearRecurrence[{24,-216,864,-1296},{0,144,3888,62208},20] (* Harvey P. Dale, Apr 29 2019 *)

From Vincenzo Librandi, Feb 12 2013: (Start)
G.f.: 144*x^2*(1+3*x)/(1-6*x)^4.
a(n) = 24*a(n-1)-216*a(n-2)+864*a(n-3)-1296*a(n-4). (End)
E.g.f.: 72*exp(6*x)*x^2*(1 + 3*x). - Stefano Spezia, Mar 08 2025

Offset corrected by Mohammad K. Azarian, Nov 20 2008

A128990 a(n) = (n^3 - n^2)*7^n.

Original entry on oeis.org

0, 196, 6174, 115248, 1680700, 21176820, 242121642, 2582630848, 26149137336, 254227724100, 2392565359030, 21924598926384, 196490913105396, 1728112389619252, 14954818756320450, 127614453387267840

Offset: 1

Mohammad K. Azarian, Apr 30 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (28, -294, 1372, -2401).

Cf. A128796, A036289.

[(n^3-n^2)*7^n: n in [1..25]]; /* or */ I:=[0,196,6174,115248]; [n le 4 select I[n] else 28*Self(n-1)-294*Self(n-2)+1372*Self(n-3)-2401*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

CoefficientList[Series[98 x (2 + 7 x)/(1 - 7 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)
LinearRecurrence[{28,-294,1372,-2401},{0,196,6174,115248},20] (* Harvey P. Dale, Mar 04 2015 *)

G.f.: 98*x^2*(2+7*x)/(1-7*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 28*a(n-1)-294*a(n-2)+1372*a(n-3)-2401*a(n-4). - Vincenzo Librandi, Feb 12 2013

Offset corrected by Mohammad K. Azarian, Nov 20 2008

cp's OEIS Frontend

A121607 (n^3+n)*3^n.

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A127369 (n^3+n)*4^n.

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A128013 a(n) = (n^3 +n)*5^n.

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A128043 (n^3+n)*6^n.

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A128048 (n^3+n)*8^n.

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Magma

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A128051 (n^3+n)*7^n.

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A128986 a(n) = (n^3 - n^2)*3^n.

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A128987 a(n) = (n^3 - n^2)*4^n.

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