A016929 -id:A016929 - cp's OEIS frontend

A016930 a(n) = (6*n + 1)^10.

1, 282475249, 137858491849, 6131066257801, 95367431640625, 819628286980801, 4808584372417849, 21611482313284249, 79792266297612001, 253295162119140625, 713342911662882601, 1822837804551761449, 4297625829703557649, 9468276082626847201, 19687440434072265625

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928, A016929.

[(6*n+1)^10: n in [0..25]]; // Vincenzo Librandi, May 04 2011

(6 Range[0, 15] + 1)^10 (* Wesley Ivan Hurt, Jan 15 2022 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1,282475249,137858491849,6131066257801,95367431640625,819628286980801,4808584372417849,21611482313284249,79792266297612001,253295162119140625,713342911662882601},20] (* Harvey P. Dale, Sep 05 2023 *)

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^10 = A016922(n)^5 = A016925(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(9, 1/6)/21941965946880. (End)

A016931 a(n) = (6*n + 1)^11.

Original entry on oeis.org

1, 1977326743, 1792160394037, 116490258898219, 2384185791015625, 25408476896404831, 177917621779460413, 929293739471222707, 3909821048582988049, 13931233916552734375, 43513917611435838661, 122130132904968017083, 313726685568359708377, 747993810527520928879

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928, A016929, A016930.

[(6*n+1)^11: n in [0..25]]; // Vincenzo Librandi, May 04 2011

(6*Range[0,20]+1)^11 (* Harvey P. Dale, Aug 23 2017 *)

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^11.
Sum_{n>=0} 1/a(n) = 1261501*Pi^11/(428554022400*sqrt(3)) + 181308931*zeta(11)/362797056. (End)

A016932 a(n) = (6*n + 1)^12.

Original entry on oeis.org

1, 13841287201, 23298085122481, 2213314919066161, 59604644775390625, 787662783788549761, 6582952005840035281, 39959630797262576401, 191581231380566414401, 766217865410400390625, 2654348974297586158321, 8182718904632857144561, 22902048046490258711521

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928, A016929, A016930, A016931.

[(6*n+1)^12: n in [0..20]]; // Vincenzo Librandi, May 04 2011

Table[(6*n + 1)^12, {n, 0, 12}] (* Amiram Eldar, Mar 28 2022 *)

From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^12 = A016922(n)^6 = A016923(n)^4 = A016924(n)^3 = A016926(n)^2.
Sum_{n>=0} 1/a(n) = PolyGamma(11, 1/6)/86890185149644800. (End)

cp's OEIS Frontend

A016930 a(n) = (6*n + 1)^10.

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A016931 a(n) = (6*n + 1)^11.

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Magma

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A016932 a(n) = (6*n + 1)^12.

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Magma

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