OFFSET
1,6
COMMENTS
From Reinhard Zumkeller, Sep 14 2014: (Start)
T(n,k) = A102473(n,k), k=1..n;
T(n,k) = A102472(n,k-n+1), k=n..2*n-1;
T(n,n) = A001040(n). (End)
LINKS
Reinhard Zumkeller, >Rows n = 1..125 of table, flattened
Russell Walsmith, CL-Chemy Transforms Fibonacci-Type Sequences to Arrays
FORMULA
The j-th column S(j) is generated by a(n+1) = (n+j)*a(n) + a(n-1), a(0)=0, a(1)=1.
EXAMPLE
Triangle begins:
1;
1, 1, 1;
1, 2, 3, 2, 1;
1, 3, 7, 10, 7, 3, 1;
...
MATHEMATICA
t[n_, n_] = 1; t[n_, k_] := t[n, k] = If[n<k, 0, (n-1)*t[n-1, k] + t[n-2, k]]; row[n_] := With[{ro = Table[t[n, k], {k, 1, n}]}, Join[Reverse[ro], Rest[ro]]]; Array[row, 8] // Flatten (* Jean-François Alcover, Oct 05 2016 *)
PROG
(Haskell)
a058294 n k = a058294_tabf !! (n-1) !! (k-1)
a058294_row n = a058294_tabf !! (n-1)
a058294_tabf = [1] : zipWith (++) xss (map (tail . reverse) xss)
where xss = tail a102473_tabl
-- Reinhard Zumkeller, Sep 14 2014
CROSSREFS
KEYWORD
nonn,tabf,nice,easy
AUTHOR
Russell Walsmith, Dec 07 2000
STATUS
approved