

A089246


Triangular array read by rows: a(n, k) is the number of ordered mtuples of positive integers (x_1, ..., x_m) such that max x_i = n+1m and there are k ones (0 <= k <= n).


9



1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 5, 5, 3, 0, 1, 14, 15, 9, 4, 0, 1, 43, 50, 31, 14, 5, 0, 1, 144, 180, 118, 54, 20, 6, 0, 1, 523, 695, 481, 229, 85, 27, 7, 0, 1, 2048, 2869, 2081, 1035, 395, 125, 35, 8, 0, 1, 8597, 12616, 9535, 4929, 1951, 629, 175, 44, 9, 0, 1, 38486, 58862
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,7


COMMENTS

The row sums are given by A047970 because row n counts the same tuples as the nth antidiagonal of A047969.


LINKS

Table of n, a(n) for n=0..67.
Mathew Englander, Comments on A101494 and A089246, and related sequences


FORMULA

From Mathew Englander, Feb 25 2021: (Start)
T(n,k) = 0^(nk) + Sum_{m = k..n1} C(m,k) * ((nm)^(mk)  (n1m)^(mk)).
T(n,k) = Sum_{j = k+1..n1} C(j,k)*Sum_{i = j..n1} T(i,j) for 0 <= k < n1; T(k+1,k)=0 and T(k,k)=1 for k>=0.
G.f. of row n: 1 + Sum_{i = 1..n} (x+ni)^(i1)*(x+ni1). (End)


EXAMPLE

a(5, 0) = 14: (5), (4,2), (2,4), (4,3), (3,4), (4,4),
(3,2,2), (2,3,2), (2,2,3), (3,3,2), (3,2,3), (2,3,3), (3,3,3), (2,2,2,2).
a(5, 1) = 15: (4,1), (1,4), (3,3,1), (3,1,3), (1,3,3), 6 permutations of (3,2,1) and 4 permutations of (2,2,2,1).
Triangle starts:
[0] 1
[1] 0, 1
[2] 1, 0, 1
[3] 2, 2, 0, 1
[4] 5, 5, 3, 0, 1
[5] 14, 15, 9, 4, 0, 1
[6] 43, 50, 31, 14, 5, 0, 1
[7] 144, 180, 118, 54, 20, 6, 0, 1
[8] 523, 695, 481, 229, 85, 27, 7, 0, 1
[9] 2048, 2869, 2081, 1035, 395, 125, 35, 8, 0, 1


CROSSREFS

Cf. A047969, A047970, A089302.
First differences by column of A101494.
Sequence in context: A188285 A273899 A102404 * A291684 A105929 A065600
Adjacent sequences: A089243 A089244 A089245 * A089247 A089248 A089249


KEYWORD

nonn,tabl,easy


AUTHOR

Alford Arnold, Dec 22 2003


EXTENSIONS

Edited and extended by David Wasserman, Sep 07 2005


STATUS

approved



