A134159 a(n) = 13 + 165*n + 756*n^2 + 1470*n^3 + 1029*n^4.

13, 3433, 31591, 130351, 370273, 846613, 1679323, 3013051, 5017141, 7885633, 11837263, 17115463, 23988361, 32748781, 43714243, 57226963, 73653853, 93386521, 116841271, 144459103, 176705713, 214071493, 257071531, 306245611

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..23.

Formula

a(n) = (3*(7*n + 2)^4 + 6*(7*n + 2)^3 - 3*(7*n + 2) + 1)/7.

a(n) = (Sum_{k=1..7n+2} k^6) / (Sum_{k=1..7n+2} k^2).

G.f.: -(13+3368*x+14556*x^2+6596*x^3+163*x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007

Mathematica

Table[(3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7, {n, 0, 100}]
Table[Sum[k^6, {k, 1, 7n + 2}]/Sum[k^2, {k, 1, 7n + 2}], {n, 0, 100}] (* Artur Jasinski *)

Crossrefs

Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134160, A134161.

Sequence in context: A260982 A159357 A221885 * A221851 A221924 A292109

Adjacent sequences: A134156 A134157 A134158 * A134160 A134161 A134162

Keyword

nonn

Author

Artur Jasinski, Oct 10 2007

Status

approved