|
|
A370380
|
|
Array read by antidiagonals: A(n,k) = (k+2)*A(n-1,k+1) + Sum_{j=0..k} A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.
|
|
1
|
|
|
1, 1, 3, 1, 5, 13, 1, 7, 29, 71, 1, 9, 51, 195, 461, 1, 11, 79, 409, 1493, 3447, 1, 13, 113, 737, 3623, 12823, 29093, 1, 15, 153, 1203, 7427, 35285, 122125, 273343, 1, 17, 199, 1831, 13601, 81009, 375591, 1277991, 2829325, 1, 19, 251, 2645, 22961, 164371
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
Array begins:
===========================================================
n\k| 0 1 2 3 4 5 6 ...
---+-------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 3 5 7 9 11 13 15 ...
2 | 13 29 51 79 113 153 199 ...
3 | 71 195 409 737 1203 1831 2645 ...
4 | 461 1493 3623 7427 13601 22961 36443 ...
5 | 3447 12823 35285 81009 164371 304667 526833 ...
6 | 29093 122125 375591 954419 2124937 4289433 8025755 ...
...
|
|
PROG
|
(PARI)
A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 1)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-1, k, (k+1)*v[k+1] + sum(j=1, k, v[j])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(6) }
|
|
CROSSREFS
|
Column k=0 is A003319 (without pair of initial terms and with different offset).
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|