OFFSET
1,5
COMMENTS
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
G. Strasser, Generalisation of the Euler adic, Math. Proc. Camb. Phil. Soc. 150 (2010) 241-256, Triangle A_5(n,k).
FORMULA
T(n, k, m) = (m*n - m*k + 1)*T(n-1, k-1, m) + (m*k - (m-1))*T(n-1, k, m), with T(t,1,m) = T(n,n,m) = 1, and m = 5.
Sum_{k=1..n} T(n, k, 5) = A047055(n-1).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 12, 1;
1, 83, 83, 1;
1, 514, 1826, 514, 1;
1, 3105, 28310, 28310, 3105, 1;
1, 18656, 376615, 905920, 376615, 18656, 1;
1, 111967, 4627821, 22403635, 22403635, 4627821, 111967, 1;
1, 671838, 54377008, 478781506, 940952670, 478781506, 54377008, 671838, 1;
MAPLE
A142460 := proc(n, k) if n = k then 1; elif k > n or k < 1 then 0 ; else (5*n-5*k+1)*procname(n-1, k-1)+(5*k-4)*procname(n-1, k) ; end if; end proc:
seq(seq(A142459(n, k), k=1..n), n=1..10) ; # R. J. Mathar, May 11 2013
MATHEMATICA
T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k -m+1)*T[n-1, k, m] ];
Table[T[n, k, 5], {n, 1, 10}, {k, 1, n}]//Flatten (* modified by G. C. Greubel, Mar 14 2022 *)
PROG
(Sage)
def T(n, k, m): # A142460
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*T(n-1, k-1, m) + (m*k-m+1)*T(n-1, k, m)
flatten([[T(n, k, 5) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Mar 14 2022
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Sep 19 2008
EXTENSIONS
Edited by N. J. A. Sloane, May 08 2013, May 11 2013
STATUS
approved