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 A134163 a(n) = 1 + 12n + 81n^3 + n(105n+ 81n^3)/2. 1
 1, 187, 1531, 5977, 16441, 36811, 71947, 127681, 210817, 329131, 491371, 707257, 987481, 1343707, 1788571, 2335681, 2999617, 3795931, 4741147, 5852761, 7149241, 8650027, 10375531, 12347137, 14587201, 17119051, 19966987, 23156281, 26713177 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A000541(n) is divisible by A000537(n) if and only n is congruent to 1 mod 3 (see A016777) LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = (3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6 a(n) = Sum[k^7]/Sum[k^3], {k, 1, 3n + 1} G.f.: -(1+182*x+606*x^2+182*x^3+x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007 MATHEMATICA Table[(3(3n + 1)^4 + 6(3n + 1)^3 - (3n + 1)^2 - 4 (3n + 1) + 2)/6, {n, 0, 100}] (* or *) Table[Sum[k^7, {k, 1, 3n + 1}]/Sum[k^3, {k, 1, 3n + 1}], {n, 0, 100}] PROG (MAGMA) [1 + 12*n + 81*n^3 + n*(105*n+ 81*n^3)/2: n in [0..30]]; // Vincenzo Librandi, May 09 2011 CROSSREFS Cf. A000537, A000541, A119617, A134153, A134154, A133180, A134158, A134159, A134160. Sequence in context: A029556 A045224 A063346 * A030536 A222911 A143661 Adjacent sequences:  A134160 A134161 A134162 * A134164 A134165 A134166 KEYWORD nonn AUTHOR Artur Jasinski, Oct 10 2007 STATUS approved

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