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A173789 a(n) is the number of (0,1) matrices A=(a_{ij}) of size n X (3n) such that each row has exactly three 1's and each column has exactly one 1 and with the restriction that no 1 stands on the diagonal from a_{11} to a_{22}. 2
0, 6, 540, 123480, 57405600, 47488518000, 63760174077600, 129947848862832000, 382114148130658944000, 1557871091922736150560000, 8528480929388117171073600000, 61063236793210618551364940160000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=0..n} (-1)^k (3n-k)!/(6^(n-k)*2^k) * binomial(n,k).
a(n) ~ sqrt(Pi) * 3^(2*n + 1/2) * n^(3*n + 1/2) / (2^(n - 1/2) * exp(3*n+1)). - Vaclav Kotesovec, Oct 21 2023
MATHEMATICA
a[n_]:= a[n]= Sum[(-1)^j*Binomial[n, j]*(3*n-j)!/(2^j*6^(n-j)), {j, 0, n}];
Table[a[n], {n, 30}] (* G. C. Greubel, Jul 13 2021 *)
Table[(3*n)! * Hypergeometric1F1[-n, -3*n, -3] / 6^n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)
PROG
(PARI) a(n)= sum(k=0, n, (-1)^k *(3*n-k)! /(6^(n-k)*2^k) * binomial(n, k)) \\ Michel Marcus, Jul 25 2013
(Sage)
def A173789(n): return sum( (-1)^j*binomial(n, j)*factorial(3*n-j)/(2^j*6^(n-j)) for j in (0..n))
[A173789(n) for n in (1..30)] # G. C. Greubel, Jul 13 2021
CROSSREFS
Sequence in context: A230330 A252174 A251697 * A258880 A367567 A121835
KEYWORD
nonn
AUTHOR
Shanzhen Gao, Feb 24 2010
STATUS
approved

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Last modified May 23 21:14 EDT 2024. Contains 372765 sequences. (Running on oeis4.)