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A174689 Triangle T(n, k) = n! * binomial(n, k)^2 - n! + 1, read by rows. 1
1, 1, 1, 1, 7, 1, 1, 49, 49, 1, 1, 361, 841, 361, 1, 1, 2881, 11881, 11881, 2881, 1, 1, 25201, 161281, 287281, 161281, 25201, 1, 1, 241921, 2217601, 6168961, 6168961, 2217601, 241921, 1, 1, 2540161, 31570561, 126403201, 197527681, 126403201, 31570561, 2540161, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, k) = n! * binomial(n, k)^2 - n! + 1.
From G. C. Greubel, Feb 10 2021: (Start)
T(n, k) = n! * ( A008459(n, k) - 1 ) + 1.
Sum_{k=0..n} T(n, k) = (n+1)*( n!*( C_{n} - 1 ) + 1 ) = (n+1)*( n!*( A000108(n) - 1 ) + 1). (End)
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 7, 1;
1, 49, 49, 1;
1, 361, 841, 361, 1;
1, 2881, 11881, 11881, 2881, 1;
1, 25201, 161281, 287281, 161281, 25201, 1;
1, 241921, 2217601, 6168961, 6168961, 2217601, 241921, 1;
1, 2540161, 31570561, 126403201, 197527681, 126403201, 31570561, 2540161, 1;
MATHEMATICA
T[n_, k_]:= n!*Binomial[n, k]^2 - n! + 1;
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Sage) flatten([[factorial(n)*(binomial(n, k)^2 -1) + 1 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 10 2021
(Magma) [Factorial(n)*(Binomial(n, k)^2 -1) + 1: k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 10 2021
CROSSREFS
Sequence in context: A178658 A156602 A203389 * A172345 A174719 A176392
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Mar 27 2010
EXTENSIONS
Edited by G. C. Greubel, Feb 10 2021
STATUS
approved

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Last modified February 21 22:13 EST 2024. Contains 370237 sequences. (Running on oeis4.)