A281946 Number of sequences of balls colored with at most n colors such that exactly two balls are of a color seen earlier in the sequence.

1, 16, 195, 2248, 26245, 318936, 4082071, 55289200, 793525833, 12063384640, 194002619371, 3294811981176, 58980720557005, 1110692723476168, 21960340413007935, 455018383693865056, 9862401602086024081, 223233406292824965360, 5268151612376938762003, 129425572759622914323880

Offset: 1

Author

Jeremy Dover, Feb 02 2017

Keywords

• nonn

Comments

Note that any such sequence has at least 3 balls and at most n+2.

Links

• Jeremy Dover, Table of n, a(n) for n = 1..100

Crossrefs

Row sums of triangle A281944.

Programs

Mathematica

Table[n! * Sum[(Binomial[k,3]+3*Binomial[k,4])/(n+2-k)!, {k, 3, n+2}], {n, 1, 20}] (* Vaclav Kotesovec, Feb 03 2017 *)

Formula

a(n) = n! * Sum_{k=3..n+2} (binomial(k,3)+3*binomial(k,4))/(n+2-k)!.

a(n)/n! ~ e*n^4/8. - Vaclav Kotesovec, Feb 03 2017