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A369527
Array read by antidiagonals: A(n,k) = (k+1)^2*A(n-1,k) + A(n-1,k+1) with A(0,k) = 1, n >= 0, k >= 0.
1
1, 1, 2, 1, 5, 7, 1, 10, 30, 37, 1, 17, 107, 227, 264, 1, 26, 298, 1261, 2169, 2433, 1, 37, 687, 5455, 16804, 25480, 27913, 1, 50, 1382, 18557, 105837, 257073, 358993, 386906, 1, 65, 2515, 52267, 516192, 2209584, 4523241, 5959213, 6346119, 1, 82, 4242, 127477
OFFSET
0,3
LINKS
Ira M. Gessel, General case of the some R-recursions, answer to question on MathOverflow (2024).
EXAMPLE
Array begins:
====================================================
n\k| 0 1 2 3 4 5 ...
---+------------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 2 5 10 17 26 37 ...
2 | 7 30 107 298 687 1382 ...
3 | 37 227 1261 5455 18557 52267 ...
4 | 264 2169 16804 105837 516192 2009089 ...
5 | 2433 25480 257073 2209584 14913889 78851808 ...
...
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^2*v[k] + v[k+1]); r[1+i] = v[1..n+1]); Mat(r)}
{ A(5) }
CROSSREFS
Column k=0 is A135920 (without initial term and with different offset).
Sequence in context: A064642 A193630 A144505 * A370382 A059039 A332022
KEYWORD
nonn,tabl,changed
AUTHOR
Mikhail Kurkov, Jan 25 2024
STATUS
approved