The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A368019 a(n) is the permanent of the n-th order Hankel matrix of Catalan numbers M(n) whose generic element is given by M(i,j) = A000108(i+j+1) with i,j = 0, ..., n-1. 7
 1, 1, 9, 979, 1417675, 28665184527, 8325587326635565, 35389363346700690999467, 2230867495754739989535874468003, 2106171270085074740753132799048111935155, 30007898337707083458776293190436074888346472515407, 6491219550166075876771081259839537013093735814742318424677245 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..11. Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn, and Carl R. Yerger, Catalan determinants-a combinatorial approach, Congressus Numerantium 200, 27-34 (2010).  On ResearchGate. M. E. Mays and Jerzy Wojciechowski, A determinant property of Catalan numbers. Discrete Math. 211, No. 1-3, 125-133 (2000). Wikipedia, Hankel matrix. FORMULA Det(M(n)) = 1 (see Mays and Wojciechowski, 2000). EXAMPLE a(4) = 1417675: 1, 2, 5, 14; 2, 5, 14, 42; 5, 14, 42, 132; 14, 42, 132, 429. MATHEMATICA Join[{1}, Table[Permanent[Table[CatalanNumber[i+j+1], {i, 0, n-1}, {j, 0, n-1}]], {n, 11}]] PROG (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108 a(n) = matpermanent(matrix(n, n, i, j, C(i+j-1))); \\ Michel Marcus, Dec 09 2023 CROSSREFS Cf. A000108. Cf. A278843, A368012, A368021, A368022, A368023, A368024, A368025. Column k=1 of A368026. Sequence in context: A087590 A048561 A361885 * A112909 A083909 A307324 Adjacent sequences: A368016 A368017 A368018 * A368020 A368021 A368022 KEYWORD nonn AUTHOR Stefano Spezia, Dec 08 2023 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 September 11 06:30 EDT 2024. Contains 375814 sequences. (Running on oeis4.)