login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293970 Number of sets of exactly eight nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter. 2

%I

%S 10,206,1926,13957,85610,476631,2477550,12289388,58942808,276126959,

%T 1272626168,5803545269,26305047510,118947441994,538263144030,

%U 2444159610896,11163194878438,51392032544011,238939873029462,1123916805738119,5357138152220234,25913264903132961

%N Number of sets of exactly eight nonempty words with a total of n letters over n-ary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

%H Alois P. Heinz, <a href="/A293970/b293970.txt">Table of n, a(n) for n = 21..816</a>

%F a(n) = [x^n y^8] Product_{j>=1} (1+y*x^j)^A000085(j).

%p g:= proc(n) option remember; `if`(n<2, 1, g(n-1)+(n-1)*g(n-2)) end:

%p b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,

%p add(b(n-i*j, i-1)*binomial(g(i), j)*x^j, j=0..n/i))), x, 9)

%p end:

%p a:= n-> coeff(b(n$2), x, 8):

%p seq(a(n), n=21..45);

%Y Column k=8 of A293815.

%Y Cf. A000085.

%K nonn

%O 21,1

%A _Alois P. Heinz_, Oct 20 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 24 21:49 EST 2022. Contains 350565 sequences. (Running on oeis4.)