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a(n) = 3^n * Sum_{i=1..n} i^3/3^i.
6

%I #19 Dec 20 2015 09:23:56

%S 1,11,60,244,857,2787,8704,26624,80601,242803,729740,2190948,6575041,

%T 19727867,59186976,177565024,532699985,1598105787,4794324220,

%U 14382980660,43148951241,129446864371,388340605280,1165021829664

%N a(n) = 3^n * Sum_{i=1..n} i^3/3^i.

%H Harry J. Smith, <a href="/A066999/b066999.txt">Table of n, a(n) for n = 1..200</a>

%F Conjecture: g.f.:(-1-x^2-4*x)/((3*x-1)*(x-1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

%F a(n) = (11*3^(n+1) - 4*n^3 - 18*n^2 - 36*n - 33)/8. - _Vaclav Kotesovec_, Nov 28 2012

%F From _Peter Bala_, Nov 29 2012: (Start)

%F Recurrence equation: a(n) = 3*a(n-1) + n^3.

%F O.g.f.: x*(1 + 4*x + x^2)/((1 - 3*x)*(1 - x)^4) = x + 11*x^2 + 244*x^3 + .... See A047520 and A067534. (End)

%t f[n_] := 3^n*Sum[i^3/3^i, {i, n}]; Array[f, 24] (* _Robert G. Wilson v_, Nov 28 2012 *)

%o (PARI) { s=0; for (n=1, 200, s+=n^3/3^n; write("b066999.txt", n, " ", 3^n*s) ) } \\ _Harry J. Smith_, Apr 25 2010

%Y Cf. A008292, A047520, A067534.

%K nonn,easy

%O 1,2

%A _Benoit Cloitre_, Jan 27 2002