OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k, m) = (m*(n-k) + 1)*T(n-1, k-1, m) + (m*k + 1)*T(n-1, k, m) - m*k*(n-k)*T(n-2, k-1, m) with T(n, 0, m) = T(n, n, m) = 1 and m = 5.
T(n, n-k, m) = T(n, k, m).
T(n, 1, 5) = A003464(n). - G. C. Greubel, Jan 10 2022
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 7, 1;
1, 43, 43, 1;
1, 259, 806, 259, 1;
1, 1555, 11720, 11720, 1555, 1;
1, 9331, 151215, 338770, 151215, 9331, 1;
1, 55987, 1828221, 7892635, 7892635, 1828221, 55987, 1;
1, 335923, 21286168, 162474781, 304389070, 162474781, 21286168, 335923, 1;
MATHEMATICA
T[n_, k_, m_]:= T[n, k, m]= If[k==0 || k==n, 1, (m*(n-k)+1)*T[n-1, k-1, m] + (m*k+1)*T[n-1, k, m] - m*k*(n-k)*T[n-2, k-1, m]];
Table[T[n, k, 5], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jan 10 2022 *)
PROG
(Sage)
@CachedFunction
def T(n, k, m): # A157156
if (k==0 or k==n): return 1
else: return (m*(n-k) +1)*T(n-1, k-1, m) + (m*k+1)*T(n-1, k, m) - m*k*(n-k)*T(n-2, k-1, m)
flatten([[T(n, k, 5) for k in (0..n)] for n in (0..20)]) # G. C. Greubel, Jan 10 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 24 2009
EXTENSIONS
Edited by G. C. Greubel, Jan 10 2022
STATUS
approved