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A091962 From enumerating paths in the plane. 5

%I

%S 0,1,42,594,4719,26026,111384,395352,1215126,3331251,8321170,19240650,

%T 41683005,85408596,166768096,312203232,563178924,982981701,1665911754,

%U 2749500754,4430505387,6985558206,10797503640,16388608600,24462014850,35952994935,52091785746

%N From enumerating paths in the plane.

%D M. de Sainte Catherine, Couplages et Pfaffiens en Combinatoire, Physique et Informatique. Ph. D. Dissertation, Universite de Bordeaux 1, 1983.

%D R. P. Stanley, Enumerative Combinatorics, volume 1 (1986), p. 221, Example 4.5.18.

%H T. D. Noe, <a href="/A091962/b091962.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Kreweras and H. Niederhausen, <a href="http://dx.doi.org/10.1016/S0195-6698(81)80020-0">Solution of an enumerative problem connected with lattice paths</a>, European J. Combin., 2 (1981), 55-60.

%H <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 a(n) = binomial(2n+6, 7)*(2n+3)*(n+1)*(n+2)/240.

%F G.f.: x*(1+31*x+187*x^2+330*x^3+187*x^4+31*x^5+x^6)/(1-x)^11. - _Colin Barker_, May 07 2012

%F a(n) = det(A*Transpose(A))/36, where A is the 2 X (n+1) matrix whose (i,j)-th element is j^(2*i-1). - _Lechoslaw Ratajczak_, Oct 01 2017

%t LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,1,42,594,4719,26026,111384,395352,1215126,3331251,8321170},30] (* _Harvey P. Dale_, Apr 15 2017 *)

%o (PARI) a(n) = binomial(2*n+6, 7)*(2*n+3)*(n+1)*(n+2)/240; \\ _Michel Marcus_, Oct 13 2016

%Y Cf. A006858.

%K nonn,easy

%O 0,3

%A _Philippe Deléham_, Mar 13 2004

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Last modified October 15 14:07 EDT 2018. Contains 316236 sequences. (Running on oeis4.)