

A028498


Let [n] = {0,...,n1}; a(n) is number of functions f:[n] > [n] for which there exists an injection g:[n] > [n+1] such that for j with 0 <= j < n, either g(j) = f(j) or g(j) = f(j)+1.


0



1, 4, 24, 186, 1770, 19980, 260820, 3863160, 63980280, 1171195200, 23476068000, 511296786000, 12021166357200, 303414507396000, 8182057223340000, 234753130435824000, 7139815170664176000, 229442416696164672000, 7767967204994540544000, 276345182709766890720000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


LINKS



FORMULA

a(n) = T(n, n) where T(1, n) = n, T(2, n) = n^2, and T(m, n) = T(m, n1) + 2*m*T(m1, n1)  m*T(m1, n2)  binomial(m, 2)*T(m2, n2) for 1 <= m <= n+1.  Sean A. Irvine, Feb 03 2020


CROSSREFS



KEYWORD

nonn


AUTHOR

Florian Lengyel (flengyel(AT)email.gc.cuny.edu)


EXTENSIONS



STATUS

approved



