%I M1988 #34 Apr 03 2018 06:26:33
%S 1,1,2,10,148,7384,1380960,1058349286
%N Intertwining numbers.
%C a(4)=10 for example is the number of ways of arranging 1 a, 2 b's, 3 c's and 4 d's so that if we look at any two letters, i and j say, with i<j, then any pair of i's are separated and surrounded by at least one j.
%C If the condition is imposed only on pairs of consecutive letters, we get A003121.
%D C. L. Mallows, Letter to _N. J. A. Sloane_, Nov 11 1980
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Georg Fischer, <a href="/A213457/a213457.txt">Perl program</a>
%e The 10 sequences for n=4 are dcbadcbdcd dcbadcdbcd dcbdacbdcd dcbdacdbcd dcbdcabdcd dcbdcadbcd dcbdcdabcd dcdbacdbcd dcdbcadbcd dcdbcdabcd.
%e For example in dcbdacdbcd we see
%e ..ba...b..
%e .cb..c.bc.
%e d.bd..db.d
%e dc.d.cd.cd
%Y Cf. A003121.
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_. Entry revised and given a new A-number by _N. J. A. Sloane_, Jun 13 2012. The old entry was A004065.
%E a(7) from _David W. Wilson_, Dec 11 1999
%E Definition clarified by _David Applegate_, Jun 14 2012
%E a(8) from _Georg Fischer_, Mar 21 2018