OFFSET
1,4
COMMENTS
If a (0,1) matrix with two 1's in each row has positive permanent, then it equals to a power of 2.
REFERENCES
V. S. Shevelev, On the permanent of the stochastic (0,1)-matrices with equal row sums, Izvestia Vuzov of the North-Caucasus region, Nature sciences 1 (1997), 21-38 (in Russian).
LINKS
Max Alekseyev, Table of n, a(n) for n = 1..100
FORMULA
a(n) = n!/4 * Sum_{l=0..n-4} binomial(n-1,l) * n^l * A000276(n-l). - Max Alekseyev, Oct 21 2024
G.f. for 4*a(n)/n!/(n-1)!: (W(-x)-ln(1+W(-x)))*(W(-x)/(1+W(-x)))^2, where W() is Lambert W-function. - Max Alekseyev, Oct 21 2024
PROG
(PARI) a174637(n) = n!*(n-1)!/4 * sum(l=0, n-4, n^l/l! * sum(i=2, n-l-2, 1/i)); \\ Max Alekseyev, Oct 21 2024
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Vladimir Shevelev, Mar 25 2010
EXTENSIONS
Incorrect formula moved to A377246 and terms a(15) onward added by Max Alekseyev, Oct 21 2024
STATUS
approved