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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

R. H. Hardin, Table of n, a(n) for n = 1..14

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

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

Adjacent sequences:  A172602 A172603 A172604 * A172606 A172607 A172608

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 06 2010

STATUS

approved

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Last modified June 24 05:21 EDT 2019. Contains 324318 sequences. (Running on oeis4.)