login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A257783 Number T(n,k) of words w of length n such that each letter of the k-ary alphabet is used at least once and for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 11
1, 0, 1, 0, 1, 2, 0, 1, 3, 6, 0, 1, 7, 12, 24, 0, 1, 12, 35, 60, 120, 0, 1, 25, 87, 210, 360, 720, 0, 1, 44, 232, 609, 1470, 2520, 5040, 0, 1, 89, 599, 1961, 4872, 11760, 20160, 40320, 0, 1, 160, 1591, 5952, 17649, 43848, 105840, 181440, 362880, 0, 1, 321, 4202, 19255, 60465, 176490, 438480, 1058400, 1814400, 3628800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row n is the inverse binomial transform of the n-th row of array A213276.

LINKS

Alois P. Heinz, Rows n = 0..20, flattened

FORMULA

T(n,k) = Sum_{i=0..k} (-1)^i * C(k,i) * A213276(n,k-i).

EXAMPLE

T(5,2) = 12: aaaab, aaaba, aaabb, aabaa, aabab, aabba, abaaa, abaab, ababa, baaaa, baaab, baaba.

Triangle T(n,k) begins:

  1;

  0, 1;

  0, 1,  2;

  0, 1,  3,   6;

  0, 1,  7,  12,   24;

  0, 1, 12,  35,   60,  120;

  0, 1, 25,  87,  210,  360,   720;

  0, 1, 44, 232,  609, 1470,  2520,  5040;

  0, 1, 89, 599, 1961, 4872, 11760, 20160, 40320;

CROSSREFS

Columns k=0-10 give: A000007, A057427, A321838, A321839, A321840, A321841, A321842, A321843, A321844, A321845, A321846.

Main diagonal gives A000142.

T(n+1,n) = A001710(n+1) (for n>0).

Cf. A213276.

Sequence in context: A195772 A330618 A062104 * A226874 A267901 A276561

Adjacent sequences:  A257780 A257781 A257782 * A257784 A257785 A257786

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, May 08 2015

STATUS

approved

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 April 19 03:20 EDT 2021. Contains 343105 sequences. (Running on oeis4.)