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 A180512 Triangle of the number of alternating sign matrices according to the number of -1's 0
 1, 2, 6, 1, 24, 16, 2, 120, 200, 94, 14, 1, 720, 2400, 2684, 1284, 310, 36, 2, 5040, 29400, 63308, 66158, 38390, 13037, 2660, 328, 26, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The first column is the factorial, A000142. The second column forms coefficients of Laguerre polynomials, A001810. From Arvind Ayyer, Mar 15 2018: (Start) Consider the row generating function A_n(x) = sum_k a(n,k) x^k. Then A_n(0) = n!, A000142. A_n(1) = number of ASM's, A005130. A_n(2) = number of domino tilings of the Aztec diamond, A006125. A_n(3) = 3-enumeration of n X n alternating-sign matrices, A059477. (End) LINKS FindStat - Combinatorial Statistic Finder, The number of entries equal to negative one in the alternating sign matrix Florent Le Gac, Quelques problèmes d’énumération autour des matrices à signes alternants, thesis, LaBRI Bordeaux, 2011. Wikipedia, Alternating Sign Matrix EXAMPLE In triangular format, the numbers of ASMs is as follows: n=1:1 n=2:2 n=3:6,1 n=4:24,16,2 n=5:120,200,94,14,1 n=6:720,2400,2684,1284,310,36,2 n=7:5040,29400,63308,66158,38390,13037,2660,328,26,1 CROSSREFS Row sums are A005130 Cf. A000142, A006125, A059477, A001810. Sequence in context: A281046 A281521 A281635 * A132181 A291646 A027642 Adjacent sequences:  A180509 A180510 A180511 * A180513 A180514 A180515 KEYWORD nonn,hard,tabf AUTHOR Arvind Ayyer, Jan 20 2011 EXTENSIONS T(7, 7) corrected by Arvind Ayyer, Feb 12 2018 STATUS approved

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Last modified August 14 06:01 EDT 2018. Contains 313748 sequences. (Running on oeis4.)