

A132812


Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(nk+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
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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,k1).  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/(nk+1);
seq(print(seq(A132812(n, k), k=0..n1)), 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



