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A123146
Triangle T(n, k) = (binomial(n,2))! / (k! * abs(k+1 - binomial(n,2))!), read by rows.
2
1, 1, 1, 3, 6, 3, 6, 30, 60, 60, 10, 90, 360, 840, 1260, 15, 210, 1365, 5460, 15015, 30030, 21, 420, 3990, 23940, 101745, 325584, 813960, 28, 756, 9828, 81900, 491400, 2260440, 8288280, 24864840, 36, 1260, 21420, 235620, 1884960, 11686752, 58433760, 242082720, 847289520
OFFSET
0,4
FORMULA
T(n, k) = (binomial(n+1,2))! / (k! * abs(k+1 - binomial(n+1,2))!).
EXAMPLE
Triangle begins as:
1;
1, 1;
3, 6, 3;
6, 30, 60, 60;
10, 90, 360, 840, 1260;
15, 210, 1365, 5460, 15015, 30030;
21, 420, 3990, 23940, 101745, 325584, 813960;
28, 756, 9828, 81900, 491400, 2260440, 8288280, 24864840;
MATHEMATICA
T[n_, k_]:= (n*(n+1)/2)!/(k!*(Abs[k+1 -(n*(n+1)/2)])!);
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(Magma) [Factorial(Binomial(n+1, 2))/(Factorial(k)*Factorial(Abs(k+1 - Binomial(n+1, 2)))): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 16 2023
(SageMath)
def A123146(n, k): return factorial(binomial(n+1, 2))/(factorial(k)*factorial(abs(k+1 - binomial(n+1, 2))))
flatten([[A123146(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jul 16 2023
CROSSREFS
Sequence in context: A323503 A303129 A170859 * A016661 A376827 A201143
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Oct 01 2006
EXTENSIONS
Edited by G. C. Greubel, Jul 16 2023
STATUS
approved