OFFSET
0,2
REFERENCES
F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 576 and 267.
LINKS
G. C. Greubel, Rows n = 0..100 of the triangle, flattened
FORMULA
T(n, k) = (-1)^k * (n-k+1)^(n+2) * binomial(n+1, k).
Sum_{k=0..n} T(n, k) = (n + 1)*(n + 2)!/2 = A001286(n+2). - G. C. Greubel, Feb 07 2021
EXAMPLE
Triangle begins as:
1;
8, -2;
81, -48, 3;
1024, -972, 192, -4;
15625, -20480, 7290, -640, 5;
279936, -468750, 245760, -43740, 1920, -6;
5764801, -11757312, 8203125, -2293760, 229635, -5376, 7;
134217728, -322828856, 282175488, -109375000, 18350080, -1102248, 14336, -8;
MATHEMATICA
T[n_, k_]:= (-1)^k*(n-k+1)^(n+2)*Binomial[n+1, k];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Sage) flatten([[ (-1)^k*(n-k+1)^(n+2)*binomial(n+1, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 07 2021
(Magma) [(-1)^k*(n-k+1)^(n+2)*Binomial(n+1, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 07 2021
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Roger L. Bagula, Apr 27 2010
EXTENSIONS
Edited by G. C. Greubel, Feb 07 2021
STATUS
approved