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!)
A261783 Number of compositions of n where each part i is marked with a word of length i over an n-ary alphabet whose letters appear in alphabetical order. 4
1, 1, 7, 73, 1031, 18501, 403495, 10366833, 306717703, 10271072557, 384058268507, 15861842372465, 717135437119271, 35228475333207937, 1868440035684996207, 106412817671933423073, 6477200889282232394759, 419626639092214594301373, 28829330550533269570699411 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..365

FORMULA

a(n) = A261780(n,n).

a(n) = [x^n] (1-x)^n/(2*(1-x)^n-1).

a(n) ~ n^n / (sqrt(2) * (log(2))^(n+1)). - Vaclav Kotesovec, Sep 21 2019

MAPLE

A:= proc(n, k) option remember; `if`(n=0, 1,

      add(A(n-j, k)*binomial(j+k-1, k-1), j=1..n))

    end:

a:= n-> A(n$2):

seq(a(n), n=0..20);

MATHEMATICA

A[n_, k_] := A[n, k] = If[n == 0, 1, Sum[A[n - j, k]*Binomial[j + k - 1, k - 1], {j, 1, n}]]; a[n_] := A[n, n]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 24 2017, translated from Maple *)

CROSSREFS

Main diagonal of A261780.

Cf. A209668.

Sequence in context: A084363 A321837 A050352 * A250917 A112939 A058350

Adjacent sequences:  A261780 A261781 A261782 * A261784 A261785 A261786

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 31 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 February 26 03:03 EST 2020. Contains 332272 sequences. (Running on oeis4.)