OFFSET
0,6
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p.194.
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = binomial(n, k)*A000166(n-k)*k^n with T(0, 0) = 1.
T(n, k) = binomial(n, k)*b(n-k)*k^n, where b(n) = n*b(n-1) + (-1)^n and b(0) = 1.
Sum_{k=0..n} T(n, k) = A137341(n).
From G. C. Greubel, Jun 10 2021: (Start)
T(n, 1) = A000240(n).
T(n, n) = A000312(n). (End)
EXAMPLE
Triangle begins as:
1;
0, 1;
0, 0, 4;
0, 3, 0, 27;
0, 8, 96, 0, 256;
0, 45, 640, 2430, 0, 3125;
0, 264, 8640, 29160, 61440, 0, 46656;
0, 1855, 118272, 688905, 1146880, 1640625, 0, 823543;
0, 14832, 1899520, 16166304, 41287680, 43750000, 47029248, 0, 16777216;
MATHEMATICA
T[n_, k_]:= If[n==0, 1, Binomial[n, k]*A000166[n-k]*k^n];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 10 2021 *)
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 15 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 10 2021
STATUS
approved