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 A091962 From enumerating paths in the plane. 5
 0, 1, 42, 594, 4719, 26026, 111384, 395352, 1215126, 3331251, 8321170, 19240650, 41683005, 85408596, 166768096, 312203232, 563178924, 982981701, 1665911754, 2749500754, 4430505387, 6985558206, 10797503640, 16388608600, 24462014850, 35952994935, 52091785746 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES M. de Sainte Catherine, Couplages et Pfaffiens en Combinatoire, Physique et Informatique. Ph. D. Dissertation, Universite de Bordeaux 1, 1983. R. P. Stanley, Enumerative Combinatorics, volume 1 (1986), p. 221, Example 4.5.18. LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 G. Kreweras and H. Niederhausen, Solution of an enumerative problem connected with lattice paths, European J. Combin., 2 (1981), 55-60. Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1). FORMULA a(n) = binomial(2n+6, 7)*(2n+3)*(n+1)*(n+2)/240. 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 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 MATHEMATICA 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 *) PROG (PARI) a(n) = binomial(2*n+6, 7)*(2*n+3)*(n+1)*(n+2)/240; \\ Michel Marcus, Oct 13 2016 CROSSREFS Cf. A006858. Sequence in context: A293096 A279888 A104901 * A269659 A007746 A200853 Adjacent sequences:  A091959 A091960 A091961 * A091963 A091964 A091965 KEYWORD nonn,easy AUTHOR Philippe Deléham, Mar 13 2004 STATUS approved

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Last modified January 22 13:50 EST 2019. Contains 319364 sequences. (Running on oeis4.)