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!)
 A142458 Triangle T(n,k) (1 <= k <= n) read by rows: T(n,k) = 1 if k=1 or k=n, else T(n,k) = (3*n-3*k+1)*T(n-1,k-1) + (3*k-2)*T(n-1,k). 35
 1, 1, 1, 1, 8, 1, 1, 39, 39, 1, 1, 166, 546, 166, 1, 1, 677, 5482, 5482, 677, 1, 1, 2724, 47175, 109640, 47175, 2724, 1, 1, 10915, 373809, 1709675, 1709675, 373809, 10915, 1, 1, 43682, 2824048, 23077694, 44451550, 23077694, 2824048, 43682, 1, 1, 174753 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Consider the triangle T(n,k) (1<=k<=n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1)+(m*k-m+1)*T(n-1,k). For m = ...,-2,-1,0,1,2,3,... we get ..., A225372, A144431, A007318, A008292, A060187, A142458, ... - N. J. A. Sloane, May 08 2013 Row sums are 1, 2, 10, 80, 880, 12320, 209440, 4188800, 96342400, 2504902400,.., (see A008544) LINKS G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_3(n,k). EXAMPLE The rows n>=1 and columns 1<=k<=n look as follows: 1; 1, 1; 1, 8, 1; 1, 39, 39, 1; 1, 166, 546, 166, 1; 1, 677, 5482, 5482, 677, 1; 1, 2724, 47175, 109640, 47175, 2724, 1; 1, 10915, 373809, 1709675, 1709675, 373809, 10915, 1; 1, 43682, 2824048, 23077694, 44451550, 23077694, 2824048, 43682, 1; 1, 174753, 20729340, 284433852, 947113254, 947113254, 284433852, 20729340, 174753, 1; MAPLE A142458 := proc(n, k) if n = k then 1; elif k > n or k < 1 then 0 ; else (3*n-3*k+1)*procname(n-1, k-1)+(3*k-2)*procname(n-1, k) ; end if; end proc: seq(seq(A142458(n, k), k=1..n), n=1..10) ; # R. J. Mathar, Jun 04 2011 MATHEMATICA A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (3*n - 3*k + 1)A[n - 1, k - 1] + (3*k - 2)A[n - 1, k]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a] CROSSREFS Cf. A225372, A144431, A007318, A008292, A060187. Sequence in context: A152972 A166346 A157640 * A174528 A259465 A176227 Adjacent sequences:  A142455 A142456 A142457 * A142459 A142460 A142461 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula, Sep 19 2008 EXTENSIONS Edited by the Associate Editors of the OEIS, Aug 28 2009 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 April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)