This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A134159 #7 Nov 16 2021 21:27:06 %S A134159 13,3433,31591,130351,370273,846613,1679323,3013051,5017141,7885633, %T A134159 11837263,17115463,23988361,32748781,43714243,57226963,73653853, %U A134159 93386521,116841271,144459103,176705713,214071493,257071531,306245611 %N A134159 a(n) = 13 + 165*n + 756*n^2 + 1470*n^3 + 1029*n^4. %C A134159 A000540(n) is divisible by A000330(n) if and only if n is congruent to {1,2,4,5} mod 7 (see A047380). A134158 is the case when n is congruent to 1 mod 7. A134159 is the case when n is congruent to 2 mod 7. A134160 is the case when n is congruent to 4 mod 7. A134161 is the case when n is congruent to 5 mod 7. A133180 is the union of A134158 and A134159 and A134160 and A134161. %F A134159 a(n) = (3*(7*n + 2)^4 + 6*(7*n + 2)^3 - 3*(7*n + 2) + 1)/7. %F A134159 a(n) = (Sum_{k=1..7n+2} k^6) / (Sum_{k=1..7n+2} k^2). %F A134159 G.f.: -(13+3368*x+14556*x^2+6596*x^3+163*x^4)/(-1+x)^5. - _R. J. Mathar_, Nov 14 2007 %t A134159 Table[(3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7, {n, 0, 100}] %t A134159 Table[Sum[k^6, {k, 1, 7n + 2}]/Sum[k^2, {k, 1, 7n + 2}], {n, 0, 100}] (* _Artur Jasinski_ *) %Y A134159 Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134160, A134161. %K A134159 nonn %O A134159 0,1 %A A134159 _Artur Jasinski_, Oct 10 2007