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A172605 Number of 7*n X 2*n 0..1 arrays with row sums 2 and column sums 7. 1
1, 936369720, 1548539246648239560000, 259207529217195001892051045386944000, 1401029485328289844705736395976227319651581140480000, 122551057241825639587910301883432838920696717566795677090154147840000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
REFERENCES
Gao, Shanzhen, and Matheis, Kenneth, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.
LINKS
FORMULA
a(n) = (1/(7!^(2n)))*Sum_{k=0..2n} Sum_{i=0..min(2n-k, floor((7n-k)/2))} Sum_{j=0..min(2n-k-i, floor((7n-k-2i)/3))} ((-1)^(j+k)*105^(i+j)*21^k*(2n)!(7n)!(14n-4i-6j-2k)!/(i!j!k!(2n-i-j-k)!(7n-2i-3j-k)!2^(7n-2i-3j-k))). - Shanzhen Gao, Feb 16 2010
a(n) ~ sqrt(Pi) * 7^(12*n + 1/2) * n^(14*n + 1/2) / (2^(n-1) * 3^(4*n) * 5^(2*n) * exp(14*n + 3)). - Vaclav Kotesovec, Oct 22 2023
MATHEMATICA
Table[1/(7!^(2*n)) * Sum[Sum[Sum[((-1)^(j+k)*105^(i+j)*21^k*(2*n)!*(7*n)!*(14*n-4*i-6*j-2*k)! / (i!*j!*k!*(2*n-i-j-k)!*(7*n-2*i-3*j-k)!*2^(7*n-2*i-3*j-k))), {j, 0, Min[2*n-k-i, Floor[(7*n-k-2*i)/3]]}], {i, 0, Min[2*n-k, Floor[(7*n-k)/2]]}], {k, 0, 2*n}], {n, 1, 12}] (* Vaclav Kotesovec, Oct 22 2023 *)
PROG
(PARI) a(n) = (1/(7!^(2*n)))*sum(k=0, 2*n, sum(i=0, min(2*n-k, floor((7*n-k)/2)), sum(j=0, min(2*n-k-i, floor((7*n-k-2*i)/3)), ((-1)^(j+k)*105^(i+j)*21^k*(2*n)!*(7*n)!*(14*n-4*i-6*j-2*k)!/(i!*j!*k!*(2*n-i-j-k)!*(7*n-2*i-3*j-k)!*2^(7*n-2*i-3*j-k)))))); \\ Michel Marcus, Jan 18 2018
CROSSREFS
Sequence in context: A115385 A186805 A122532 * A015394 A114261 A321489
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 06 2010
STATUS
approved

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Last modified July 15 07:59 EDT 2024. Contains 374324 sequences. (Running on oeis4.)