A366488 a(n) = (n^11 - n)/11.

0, 0, 186, 16104, 381300, 4438920, 32981550, 179756976, 780903144, 2852823600, 9090909090, 25937424600, 67546215516, 162923672184, 368142288150, 786341441760, 1599289640400, 3115626937056, 5842582734474, 10590023536200, 18618181818180, 31843409140200, 53119845582846, 86619068901264, 138334649379000, 216744162819600

Offset: 0

Author

N. J. A. Sloane, Nov 13 2023

Keywords

• nonn
• easy

Comments

If p is a prime, (n^p-n)/p is an integer by Fermat's Little Theorem. For p = 2, 3, 5, 7, ..., this gives A000217, A007290, A208536, A208537, this sequence, A366489, A366490, A366491.

Links

• Stefano Spezia, Table of n, a(n) for n = 0..10000
• Jack Jeffries, Differentiating by prime numbers, Notices Amer. Math. Soc., 70:11 (2023), 1772-1779.
• Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Crossrefs

Cf. A000217, A007290, A208536, A208537, A366489, A366490, A366491.

Programs

Mathematica

A366488[n_]:=(n^11-n)/11;Array[A366488,30,0] (* Paolo Xausa, Nov 14 2023 *)
LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{0,0,186,16104,381300,4438920,32981550,179756976,780903144,2852823600,9090909090,25937424600},30] (* Harvey P. Dale, Aug 03 2025 *)

Formula

a(n) == 0 (mod 6). - Hugo Pfoertner, Nov 14 2023