A382820 Number of columns in all n-compositions of n.

1, 11, 163, 3019, 67251, 1753877, 52468711, 1772042699, 66708748963, 2770212058261, 125812351808551, 6203908746628501, 330108021642012407, 18853083403505443593, 1150352428059538611663, 74685045367715777653195, 5140745255774277374241411, 373950591013899715795929605

Offset

1,2

Comments

A k-composition of n is a rectangular array of nonnegative integers with k rows, at least one nonzero entry in each column, and having the sum of all entries equal to n.

Links

Table of n, a(n) for n=1..18.

Formula

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

Prog

(PARI)
A382818_Column(k, N) = {my(x='x+O('x^N)); Vec(-(((1 - x)^k - 1)*(1 - x)^k)/( ((1 - x)^k - 1) + (1 - x)^k)^2)}
A382820(n)= {A382818_Column(n, n+1)[n]}

Crossrefs

Cf. A001792, A145839, A181289, A181290, (main diagonal of A382818).

Sequence in context: A370911 A141876 A174364 * A229963 A051619 A261504

Adjacent sequences: A382817 A382818 A382819 * A382821 A382822 A382823

Keyword

nonn,easy

Author

John Tyler Rascoe, Apr 05 2025

Status

approved