The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A095801 Square of Narayana triangle A001263: View A001263 as a lower triangular matrix. Then the square of that matrix is also lower triangular. Sequence gives this lower triangle, read by rows. 1
 1, 2, 1, 5, 6, 1, 14, 30, 12, 1, 42, 140, 100, 20, 1, 132, 630, 700, 250, 30, 1, 429, 2772, 4410, 2450, 525, 42, 1, 1430, 12012, 25872, 20580, 6860, 980, 56, 1, 4862, 51480, 144144, 155232, 74088, 16464, 1680, 72, 1, 16796, 218790, 772200, 1081080, 698544 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The first three columns are A000108 (the Catalan numbers), A002457 and A085374. LINKS Table of n, a(n) for n=1..50. FORMULA T(n, k) = Sum_{i = k..n} A001263(n, i)*A001263(i, k). T(n, n-1) = n*(n-1). EXAMPLE The first 3 rows are 1; 2, 1; 5, 6, 1; since the first 3 rows of the Narayana triangle in matrix format are M = [1 0 0 / 1 1 0 / 1 3 1]. Then M^2 = [1 0 0 / 2 1 0 / 5 6 1]. Triangle starts: 1; 2, 1; 5, 6, 1; 14, 30, 12, 1; 42, 140, 100, 20, 1; ... MATHEMATICA t[n_, k_] = Sum[1/(i*k)*(Binomial[i-1, k-1]*Binomial[i, k-1]* Binomial[n-1, i-1]*Binomial[n, i-1]), {i, k, n}]; Flatten[Table[t[n, k], {n, 1, 10}, {k, 1, n}]][[1;; 50]] (* Jean-François Alcover, Jul 21 2011 *) CROSSREFS Cf. A000108, A001263, A002457, A085374. Sequence in context: A107783 A047887 A120986 * A128567 A345394 A217204 Adjacent sequences: A095798 A095799 A095800 * A095802 A095803 A095804 KEYWORD nonn,easy,nice,tabl AUTHOR Gary W. Adamson, Jun 07 2004 EXTENSIONS Edited and extended by David Wasserman, Sep 24 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 22 15:18 EDT 2024. Contains 372758 sequences. (Running on oeis4.)