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 A132812 Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1). 7
 1, 2, 2, 3, 9, 3, 4, 24, 24, 4, 5, 50, 100, 50, 5, 6, 90, 300, 300, 90, 6, 7, 147, 735, 1225, 735, 147, 7, 8, 224, 1568, 3920, 3920, 1568, 224, 8, 9, 324, 3024, 10584, 15876, 10584, 3024, 324, 9, 10, 450, 5400, 25200, 52920, 52920, 25200, 5400, 450, 10 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A127648 * A001263. (Original name by Gary W. Adamson.) Let a meander be defined as in the link and m = 2. Then T(n,k) counts the invertible meanders of length m(n+1) built from arcs with central angle 360/m whose binary representation have mk '1's. - Peter Luschny, Dec 19 2011 Antidiagonal sums = A110320. - Philippe Deléham, Jun 08 2013 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1..150). Peter Luschny, Meanders. FORMULA A127648 * A001263 as infinite lower triangular matrices. a(n) = n * A001263(n,k). T(n,k) = binomial(n,k)*binomial(n,k-1). - Philippe Deléham, Jun 08 2013 EXAMPLE First few rows of the triangle are: 1; 2, 2; 3, 9, 3; 4, 24, 24, 4; 5, 50, 100, 50, 5; 6, 90, 300, 300, 90, 6; ... Row 4 = (4, 24, 24, 4) = 4 * (1, 6, 6, 1), where (1, 6, 6, 1) = row 4 of the Narayana triangle. - Gary W. Adamson T(3,1) = 3 because the invertible meanders of length 8 and central angle 180 degree which have two '1's in their binary representation are {10000100, 10010000, 11000000}. - Peter Luschny, Dec 19 2011 MAPLE A132812 := (n, k) -> k*binomial(n, k)^2/(n-k+1); seq(print(seq(A132812(n, k), k=0..n-1)), n=1..6); # Peter Luschny, Dec 19 2011 MATHEMATICA Table[k Binomial[n, k]^2/(n - k + 1), {n, 10}, {k, n}] // Flatten (* Michael De Vlieger, Nov 15 2017 *) CROSSREFS Row sums: A001791. Cf. A001263, A127648, A001791, A202409. Sequence in context: A184844 A252848 A241475 * A203371 A181206 A274959 Adjacent sequences:  A132809 A132810 A132811 * A132813 A132814 A132815 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Sep 01 2007 EXTENSIONS New name from Peter Luschny, Dec 19 2011 a(53) corrected by Michael De Vlieger, Nov 15 2017 STATUS approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)