

A134158


a(n)=1 + 27n + 252n^2 + 882n^3 + 1029n^4.


6



1, 2191, 24583, 109513, 324013, 759811, 1533331, 2785693, 4682713, 7414903, 11197471, 16270321, 22898053, 31369963, 42000043, 55126981, 71114161, 90349663, 113246263, 140241433, 171797341, 208400851, 250563523, 298821613
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OFFSET

0,2


COMMENTS

A000540(n) is divisible by A000330(n) if and only n is congruent to {1,2,4,5} mod 7 (see A047380) A134158 is case when n is congruent to 1 mod 7 A134159 is case when n is congruent to 2 mod 7 A134160 is case when n is congruent to 4 mod 7 A134161 is case when n is congruent to 5 mod 7 A133180 is union of A134158 and A134159 and A134160 and A134161


LINKS

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


FORMULA

a(n) = (3(7n + 1)^4 + 6(7n + 1)^3  3 (7n + 1) + 1)/7 a(n) = Sum[k^6]/Sum[k^2], {k, 1, 7n + 1}]
G.f.: (1+2186*x+13638*x^2+8498*x^3+373*x^4)/(1+x)^5.  R. J. Mathar, Nov 14 2007


MATHEMATICA

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


CROSSREFS

Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134159, A134160, A134161.
Sequence in context: A081865 A085442 A208549 * A227488 A225719 A229319
Adjacent sequences: A134155 A134156 A134157 * A134159 A134160 A134161


KEYWORD

nonn


AUTHOR

Artur Jasinski, Oct 10 2007


STATUS

approved



