A282060
Coefficients in q-expansion of E_4*(E_2*E_4 - E_6)/720, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
Original entry on oeis.org
0, 1, 258, 6564, 66052, 390630, 1693512, 5764808, 16909320, 43066413, 100782540, 214358892, 433565328, 815730734, 1487320464, 2564095320, 4328785936, 6975757458, 11111134554, 16983563060, 25801892760, 37840199712, 55304594136, 78310985304, 110992776480
Offset: 0
a(6) = 1^8*6^1 + 2^8*3^1 + 3^8*2^1 + 6^8*1^1 = 1693512.
-
terms = 25;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E4[x]*(E2[x]*E4[x] - E6[x])/720 + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
Table[n * DivisorSigma[7, n], {n, 0, 24}] (* Amiram Eldar, Sep 06 2023 *)
nmax = 40; CoefficientList[Series[x*Sum[k^8*x^(k-1)/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 01 2025 *)
-
a(n) = if(n < 1, 0, n*sigma(n, 7)) \\ Andrew Howroyd, Jul 25 2018
A196289
a(n) = n^9 - n.
Original entry on oeis.org
0, 0, 510, 19680, 262140, 1953120, 10077690, 40353600, 134217720, 387420480, 999999990, 2357947680, 5159780340, 10604499360, 20661046770, 38443359360, 68719476720, 118587876480, 198359290350, 322687697760, 511999999980, 794280046560, 1207269217770, 1801152661440, 2641807540200
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
-
[n^9-n: n in [0..30]];
-
Table[n^9 - n, {n, 0, 40}] (* and *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 0, 510, 19680, 262140, 1953120, 10077690, 40353600, 134217720, 387420480}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2012 *)
-
a(n)=n^9-n \\ Charles R Greathouse IV, Nov 21 2011
A196290
a(n) = n^9 + n.
Original entry on oeis.org
0, 2, 514, 19686, 262148, 1953130, 10077702, 40353614, 134217736, 387420498, 1000000010, 2357947702, 5159780364, 10604499386, 20661046798, 38443359390, 68719476752, 118587876514, 198359290386, 322687697798, 512000000020, 794280046602, 1207269217814, 1801152661486, 2641807540248
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
A196291
a(n) = n^10 - n.
Original entry on oeis.org
0, 0, 1022, 59046, 1048572, 9765620, 60466170, 282475242, 1073741816, 3486784392, 9999999990, 25937424590, 61917364212, 137858491836, 289254654962, 576650390610, 1099511627760, 2015993900432, 3570467226606, 6131066257782, 10239999999980, 16679880978180, 26559922791402, 41426511213626
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
-
[n^10-n: n in [0..30]];
-
Table[n^10 - n, {n, 0, 40}] (* and *) LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 0, 1022, 59046, 1048572, 9765620, 60466170, 282475242, 1073741816, 3486784392, 9999999990}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2012 *)
-
a(n)=n^10-n \\ Charles R Greathouse IV, Nov 22 2011
A196292
a(n) = n^10 + n.
Original entry on oeis.org
0, 2, 1026, 59052, 1048580, 9765630, 60466182, 282475256, 1073741832, 3486784410, 10000000010, 25937424612, 61917364236, 137858491862, 289254654990, 576650390640, 1099511627792, 2015993900466, 3570467226642, 6131066257820, 10240000000020, 16679880978222, 26559922791446
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Showing 1-5 of 5 results.
Comments