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A174690 Triangle T(n, k) = n!*binomial(n, k) - n! + 1, read by rows. 2
1, 1, 1, 1, 3, 1, 1, 13, 13, 1, 1, 73, 121, 73, 1, 1, 481, 1081, 1081, 481, 1, 1, 3601, 10081, 13681, 10081, 3601, 1, 1, 30241, 100801, 171361, 171361, 100801, 30241, 1, 1, 282241, 1088641, 2217601, 2782081, 2217601, 1088641, 282241, 1, 1, 2903041, 12700801, 30119041, 45360001, 45360001, 30119041, 12700801, 2903041, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, k) = n!*binomial(n, k) - n! + 1.
From G. C. Greubel, Feb 09 2021: (Start)
T(n, k) = A196347(n, k) - n! + 1 = (-1)^k * A021012(n, k) - n! + 1.
Sum_{k=0..n} T(n, k) = 2^n * n! - (n+1)! + (n+1) = A000165(n) - (n+1)! + (n+1). (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 3, 1;
1, 13, 13, 1;
1, 73, 121, 73, 1;
1, 481, 1081, 1081, 481, 1;
1, 3601, 10081, 13681, 10081, 3601, 1;
1, 30241, 100801, 171361, 171361, 100801, 30241, 1;
1, 282241, 1088641, 2217601, 2782081, 2217601, 1088641, 282241, 1;
MATHEMATICA
T[n_, k_]:= n!*Binomial[n, k] - n! + 1;
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Sage) flatten([[factorial(n)*(binomial(n, k) -1) + 1 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 09 2021
(Magma) [Factorial(n)*(Binomial(n, k) -1) + 1: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 09 2021
CROSSREFS
Sequence in context: A055154 A338875 A015112 * A156869 A153090 A203002
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Mar 27 2010
EXTENSIONS
Edited by G. C. Greubel, Feb 09 2021
STATUS
approved

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Last modified April 25 10:22 EDT 2024. Contains 371967 sequences. (Running on oeis4.)