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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}. 1
0, 6, 540, 123480, 57405600, 47488518000, 63760174077600, 129947848862832000, 382114148130658944000, 1557871091922736150560000, 8528480929388117171073600000, 61063236793210618551364940160000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..150

FORMULA

a(n) = Sum_{k=0..n} (-1)^k (3n-k)!/(6^(n-k)*2^k) * binomial(n,k).

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 *)

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

Cf. A173790, A173791.

Sequence in context: A230330 A252174 A251697 * A258880 A121835 A159531

Adjacent sequences:  A173786 A173787 A173788 * A173790 A173791 A173792

KEYWORD

nonn

AUTHOR

Shanzhen Gao, Feb 24 2010

STATUS

approved

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Last modified June 26 13:24 EDT 2022. Contains 354883 sequences. (Running on oeis4.)