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A016780
a(n) = (3*n+1)^4.
11
1, 256, 2401, 10000, 28561, 65536, 130321, 234256, 390625, 614656, 923521, 1336336, 1874161, 2560000, 3418801, 4477456, 5764801, 7311616, 9150625, 11316496, 13845841, 16777216, 20151121, 24010000, 28398241, 33362176, 38950081, 45212176, 52200625, 59969536, 68574961
OFFSET
0,2
FORMULA
From Harvey P. Dale, Oct 21 2015: (Start)
a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5).
G.f.: -((1+251*x+1131*x^2+545*x^3+16*x^4)/(-1+x)^5). (End)
a(n) = A000583(A016777(n)). - Michel Marcus, Nov 06 2015
E.g.f.: exp(x)*(1+255*x+945*x^2+594*x^3+81*x^4). - Wolfdieter Lang, Apr 02 2017
Sum_{n>=0} 1/a(n) = PolyGamma(3, 1/3)/486. - Amiram Eldar, Mar 29 2022
MATHEMATICA
(3*Range[0, 30]+1)^4 (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 256, 2401, 10000, 28561}, 30] (* Harvey P. Dale, Oct 21 2015 *)
PROG
(Magma) [(3*n+1)^4: n in [0..30]]; // Vincenzo Librandi, Sep 21 2011
CROSSREFS
Cf. A000583 (n^4), A016777 (3n+1), A016778, A016779, A016781.
Sequence in context: A236087 A204303 A236083 * A236041 A236037 A251120
KEYWORD
nonn,easy
AUTHOR
STATUS
approved