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A259435 a(n) = 2*(n-1)^6*(n+1)^2*(n^2+10*n+1).

%I A259435 #18 Dec 29 2024 17:40:44
%S A259435 2,0,450,81920,2077650,22413312,148531250,716636160,2763575010,
%T A259435 9017753600,25850353122,66816000000,158678718770,351151718400,
%U A259435 731985584850,1449526034432,2745436781250,5000952545280,8800799033090,15019798118400,24938174692242,40392704000000
%N A259435 a(n) = 2*(n-1)^6*(n+1)^2*(n^2+10*n+1).
%C A259435 This appears as the function alpha(n) in Delest, related to bar/bat theory; see section 3.
%H A259435 M. P. Delest, <a href="http://dx.doi.org/10.1016/0097-3165(88)90071-4">Generating functions for column-convex polyominoes</a>, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression E in Theorem 16 page 29.
%H A259435 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F A259435 G.f.: 2*(1 -11*x + 280*x^2 + 38320*x^3 + 600970*x^4 + 1994794*x^5 + 1444096*x^6 - 231320*x^7 - 207395*x^8 - 10935*x^9)/(1-x)^11.
%F A259435 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).
%p A259435 A259435:=n->2*(n-1)^6*(n+1)^2*(n^2+10*n+1): seq(A259435(n), n=0..30); # _Wesley Ivan Hurt_, Jun 29 2015
%t A259435 Table[2 (n - 1)^6 (n + 1)^2 (n^2 + 10 n + 1), {n, 0, 30}]
%t A259435 LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{2,0,450,81920,2077650,22413312,148531250,716636160,2763575010,9017753600,25850353122},30] (* _Harvey P. Dale_, Dec 29 2024 *)
%o A259435 (Magma) [2*(n-1)^6*(n+1)^2*(n^2+10*n+1): n in [0..30]];
%o A259435 (PARI) a(n)=2*(n-1)^6*(n+1)^2*(n^2+10*n+1) \\ _Charles R Greathouse IV_, Jun 29 2015
%o A259435 (Sage) [2*(n-1)^6*(n+1)^2*(n^2+10*n+1) for n in (0..30)] # _Bruno Berselli_, Jun 30 2015
%Y A259435 Cf. A001105, A005435, A259364, A259395.
%K A259435 nonn,easy
%O A259435 0,1
%A A259435 _Vincenzo Librandi_, Jun 27 2015