A369527 - OEIS

A369527

Array read by downward 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, 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, 2009089, 14913889, 50267233, 90976402, 114813254, 121159373

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..54.

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

Adjacent sequences: A369524 A369525 A369526 * A369528 A369529 A369530

KEYWORD

nonn,tabl,changed

AUTHOR

Mikhail Kurkov, Jan 25 2024

STATUS

approved