OFFSET
0,2
FORMULA
Conjecture: A(n,0) = A258173(n+1). - Mikhail Kurkov, Oct 27 2024
A(n,k) = A(n,k-1) + (A(n,k-1) - A(n-1,k))/k + k*A(n-1,k) + A(n-1,k+1) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = k+1. - Mikhail Kurkov, Nov 24 2024
EXAMPLE
Array begins:
==============================================================
n\k| 0 1 2 3 4 5 6 ...
---+----------------------------------------------------------
0 | 1 2 3 4 5 6 7 ...
1 | 3 9 22 45 81 133 204 ...
2 | 12 46 147 397 933 1962 3776 ...
3 | 58 263 1012 3341 9637 24758 57678 ...
4 | 321 1654 7340 28333 96313 292092 800991 ...
5 | 1975 11290 56278 246905 961897 3357309 10601156 ...
6 | 13265 82808 455534 2227689 9749034 38415080 137251108 ...
...
PROG
(PARI)
A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, k)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-1, k, v[k+1] + k*sum(j=1, k, v[j])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(6) }
CROSSREFS
KEYWORD
AUTHOR
Mikhail Kurkov, Mar 28 2024
STATUS
approved