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, 5) = T(n, k, 5).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 17, 1;
1, 123, 123, 1;
1, 769, 3046, 769, 1;
1, 4655, 49500, 49500, 4655, 1;
1, 27981, 673015, 1721070, 673015, 27981, 1;
1, 167947, 8363421, 44640435, 44640435, 8363421, 167947, 1;
1, 1007753, 98882848, 982172031, 2012583870, 982172031, 98882848, 1007753, 1;
MAPLE
A157151:= proc(n, k)
if k<0 or n<k then 0;
elif k=0 or k=n then 1;
else (5*n-5*k+1)*procname(n-1, k-1) + (5*k+1)*procname(n-1, k) + 5*k*(n-k)*procname(n-2, k-1);
end if; end proc;
seq(seq(A157151(n, k), k=0..n), n=0..10); # R. J. Mathar, Feb 06 2015
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 09 2022 *)
PROG
(Sage)
def T(n, k, m): # A157147
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..10)]) # G. C. Greubel, Jan 09 2022
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Feb 24 2009
EXTENSIONS
Edited by G. C. Greubel, Jan 09 2022
STATUS
approved