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A371567
Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + (k+1)*Sum_{j=0..k} A(n-1,j) with A(0,k) = k+1, n >= 0, k >= 0.
1
1, 2, 3, 3, 9, 12, 4, 22, 46, 58, 5, 45, 147, 263, 321, 6, 81, 397, 1012, 1654, 1975, 7, 133, 933, 3341, 7340, 11290, 13265, 8, 204, 1962, 9637, 28333, 56278, 82808, 96073, 9, 297, 3776, 24758, 96313, 246905, 455534, 647680, 743753, 10, 415, 6767, 57678, 292092, 961897, 2227689, 3882510, 5370016, 6113769
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
Cf. A258173.
Sequence in context: A248788 A340914 A194232 * A110042 A306101 A364967
KEYWORD
nonn,tabl,changed
AUTHOR
Mikhail Kurkov, Mar 28 2024
STATUS
approved