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 A021010 Triangle of coefficients of Laguerre polynomials L_n(x) (powers of x in decreasing order). 6
 1, -1, 1, 1, -4, 2, -1, 9, -18, 6, 1, -16, 72, -96, 24, -1, 25, -200, 600, -600, 120, 1, -36, 450, -2400, 5400, -4320, 720, -1, 49, -882, 7350, -29400, 52920, -35280, 5040, 1, -64, 1568, -18816, 117600, -376320, 564480, -322560, 40320, -1, 81, -2592 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS abs(T(n,k))=k!*binomial(n,k)^2=number of k-matchings of the complete bipartite graph K_{n,n}. Example: abs(T(2,2))=2 because in the bipartite graph K_{2,2} with vertex sets {A,B},{A',B'} we have the 2-matchings {AA',BB'} and {AB',BA'}. Row sums of the absolute values yield A002720. - Emeric Deutsch, Dec 25 2004 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 799. LINKS T. D. Noe, Rows n=0..50 of triangle, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. Eric Weisstein's World of Mathematics, Rook Polynomial FORMULA T(n, k)=(-1)^(n-k)*k!*binomial(n, k)^2. - Emeric Deutsch, Dec 25 2004 EXAMPLE 1; -1,1; 1,-4,2; -1,9,-18,6; 1,-16,72,-96,24; ... MAPLE T:=(n, k)->(-1)^(n-k)*k!*binomial(n, k)^2: for n from 0 to 9 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form (Deutsch) MATHEMATICA Flatten[ Table[ Reverse[ CoefficientList[n!*LaguerreL[n, x], x]], {n, 0, 9}]] (* From Jean-François Alcover, Nov 24 2011 *) CROSSREFS Cf. A021009, A002720. Sequence in context: A211957 A063983 A144084 * A193607 A075397 A049429 Adjacent sequences:  A021007 A021008 A021009 * A021011 A021012 A021013 KEYWORD sign,tabl,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers STATUS approved

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