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A156047
Triangle read by rows: T(n, k) = (n+1)!*(1/k + 1/(n-k+1)).
1
4, 9, 9, 32, 24, 32, 150, 100, 100, 150, 864, 540, 480, 540, 864, 5880, 3528, 2940, 2940, 3528, 5880, 46080, 26880, 21504, 20160, 21504, 26880, 46080, 408240, 233280, 181440, 163296, 163296, 181440, 233280, 408240, 4032000, 2268000, 1728000, 1512000, 1451520, 1512000, 1728000, 2268000, 4032000
OFFSET
1,1
COMMENTS
Row sums are (n+1)*A052517(n+2) = {4, 18, 88, 500, 3288, 24696, 209088, 1972512, 20531520, ...}.
FORMULA
T(n, k) = (n+1)*(n+1)!/(k*(n-k+1)).
Sum_{k=1..n} T(n,k) = 2*(n+1)!*H(n), where H(n) is the harmonic number. - G. C. Greubel, Dec 02 2019
EXAMPLE
Triangle begins as:
4;
9, 9;
32, 24, 32;
150, 100, 100, 150;
864, 540, 480, 540, 864;
5880, 3528, 2940, 2940, 3528, 5880;
46080, 26880, 21504, 20160, 21504, 26880, 46080;
MAPLE
seq(seq( (n+1)*(n+1)!/(k*(n-k+1)), k=1..n), n=1..10); # G. C. Greubel, Dec 02 2019
MATHEMATICA
Table[(n+1)*(n+1)!/(k*(n-k+1)), {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Dec 02 2019 *)
PROG
(PARI) T(n, k) = (n+1)*(n+1)!/(k*(n-k+1)); \\ G. C. Greubel, Dec 02 2019
(Magma) [(n+1)*Factorial(n+1)/(k*(n-k+1)): k in [1..n], n in [1..10]]; // G. C. Greubel, Dec 02 2019
(Sage) [[(n+1)*factorial(n+1)/(k*(n-k+1)) for k in (1..n)] for n in (1..10)] # G. C. Greubel, Dec 02 2019
(GAP) Flat(List([1..10], n-> List([1..n], k-> (n+1)*Factorial(n+1)/(k*(n-k+1)) ))); # G. C. Greubel, Dec 02 2019
CROSSREFS
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Feb 02 2009
EXTENSIONS
Offset changed by G. C. Greubel, Dec 02 2019
STATUS
approved