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a(n) = Stirling_2(n,3)^2.
1

%I #28 Dec 07 2019 12:18:25

%S 0,0,0,1,36,625,8100,90601,933156,9150625,87048900,812307001,

%T 7486748676,68447640625,622473660900,5641104760201,51003678922596,

%U 460438253730625,4152386009780100,37422167780506201,337103845136750916,3035761307578140625,27332814735512302500

%N a(n) = Stirling_2(n,3)^2.

%H H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/website/dek.pdf">A lot of toast, with a side order of roast</a>, manuscript, Jan 04 2002.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (25,-239,1115,-2664,3060,-1296).

%F G.f.: x^3*(1+11*x-36*x^2-36*x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-6*x)*(1-9*x)).

%F a(n) = (3^n - 3*2^n + 3)^2/36 for n>0. - _Charles R Greathouse IV_, Jan 03 2013

%t StirlingS2[Range[0,30],3]^2 (* _Harvey P. Dale_, Jan 03 2013 *)

%o (Sage)[stirling_number2(n,3)^2for n in range(0,23)] # _Zerinvary Lajos_, Mar 14 2009

%o (PARI) a(n)=(3^n-3<<n+3)^2/36 \\ _Charles R Greathouse IV_, Jan 03 2013

%Y Cf. A000392.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_, Feb 08 2008

%E Definition corrected (exponent changed from 3 to 2) by _Harvey P. Dale_, Jan 03 2013