The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A196846 Table of elementary symmetric functions a_k(1,2,5,6,...,n+2) (no 3,4). 2
 1, 1, 1, 1, 3, 2, 1, 8, 17, 10, 1, 14, 65, 112, 60, 1, 21, 163, 567, 844, 420, 1, 29, 331, 1871, 5380, 7172, 3360, 1, 38, 592, 4850, 22219, 55592, 67908, 30240, 1, 48, 972, 10770, 70719, 277782, 623828, 709320, 302400, 1, 59, 1500, 21462, 189189, 1055691, 3679430, 7571428, 8104920, 3326400 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For the symmetric functions a_k see a comment in A196841. The definition of the family of number triangles S_{i,j}(n,k),n>=k>=0, 1<=i=3; k=0..n, with the elementary symmetric functions a_k (see the comment above). a(n,k) = |s(n+1,n+1-k)| for 0<=n<3, a(n,k) = sum(((3*4)^m)*(|s(n+3,n+3-k+2*m)| - (3*S_3(n+1,k-1-2*m) + 4*S_4(n+1,k-1-2*m))),m = 0..floor(k/2)), with the Stirling numbers of the first kind s(n,m) = A048994(n,m), and the number triangles S_3(n,k)= A196842(n,k) and S_4(n,k)= A196843(n,k) (for negative k one puts the entries of these triangles to 0). EXAMPLE n\k   0    1    2     3      4      5      6       7 ... 0:    1 1:    1    1 2:    1    3    2 3:    1    8   17    10 4:    1   14   65   112     60 5:    1   21  163   567    844    420 6:    1   29  331  1871   5380   7172   3360 7:    1   38  592  4850  22219  55592  67908   30240 ... a(2,2)=a_2(1,2)=A094638(3,3)=1*2=2. a(2,2) = |s(3,1)| = 2. a(4,2) = a_2(1,2,5,6) = 1*2+1*5+1*6+2*5+2*6+5*6 = 65. a(4,2) = 1*(|s(7,5)| - (3*S_3(5,1) + 4*S_4(5,1))) + 3*4*(|s(7,7)| -(3*0 + 4*0)) = 1*(175 -(3*18 + 4*17)) + 12*1 = 65. CROSSREFS Cf. A094638 (a_k triangle), A196845 (no 1,2 triangle), A196842 (no 3), A196843 (no 4). Sequence in context: A204144 A203992 A204019 * A101413 A101908 A290310 Adjacent sequences:  A196843 A196844 A196845 * A196847 A196848 A196849 KEYWORD nonn,easy,tabl AUTHOR Wolfdieter Lang, Oct 27 2011 STATUS approved

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

Last modified September 19 19:41 EDT 2021. Contains 347564 sequences. (Running on oeis4.)