OFFSET
1,2
FORMULA
a(n) = binomial(k,4)*n!*(1/(n+3-k)! + 3/(n+2-k)!) (with the convention that 3/(-1)! = 0 when k=n+3).
EXAMPLE
For n=1: AAAA -> T(1,4)=1.
For n=2: AAAA,BBBB,AABB,ABAB,ABBA,BAAB,BABA,BBAA -> T(2,4)=8; AAAAB,AAABA,AABAA,ABAAA,BAAAA,BBBBA,BBBAB,BBABB,BABBB,ABBBB -> T(2,5)=10.
Triangle starts:
1;
8, 10;
21, 120, 90;
40, 420, 1440, 840;
65, 1000, 6300, 16800, 8400;
96, 1950, 18000, 88200, 201600, 90720;
133, 3360, 40950, 294000, 1234800, 2540160, 1058400;
176, 5320, 80640, 764400, 4704000, 17781120, 33868800, 13305600;
225, 7920, 143640, 1693440, 13759200, 76204800, 266716800, ... .
MATHEMATICA
Table[Binomial[k, 4] n! (1/(n + 3 - k)! + 3/(n + 2 - k)!), {n, 9}, {k, 4, n + 3}] // Flatten (* Michael De Vlieger, Sep 30 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jeremy Dover, Sep 27 2017
STATUS
approved