A379460 Array read by downward antidiagonals: A(n,k) = A(n,k-1) + (k+1)*(A(n-1,k) + A(n-1,k+1)) with A(n,0) = A(n-1,0) + A(n-1,1), A(0,k) = 1, n >= 0, k >= 0.

1, 1, 2, 1, 6, 8, 1, 12, 44, 52, 1, 20, 140, 420, 472, 1, 30, 340, 1860, 5032, 5504, 1, 42, 700, 6020, 28672, 72912, 78416, 1, 56, 1288, 15960, 116592, 508704, 1241648, 1320064, 1, 72, 2184, 36792, 380352, 2496480, 10257200, 24317760, 25637824, 1, 90, 3480, 76440, 1059744, 9696960, 59030960, 232182240, 538637824, 564275648

Offset: 0

Author

Mikhail Kurkov, Dec 23 2024

Keywords

• nonn
• tabl

Examples

			Array begins:
=============================================================
n\k|     0       1        2        3         4          5 ...
---+---------------------------------------------------------
0  |     1       1        1        1         1          1 ...
1  |     2       6       12       20        30         42 ...
2  |     8      44      140      340       700       1288 ...
3  |    52     420     1860     6020     15960      36792 ...
4  |   472    5032    28672   116592    380352    1059744 ...
5  |  5504   72912   508704  2496480   9696960   31778208 ...
  ...
		

Crossrefs

Cf. A006351.

Programs

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[1] = v[1] + v[2]; for(k=2, #v-1, v[k] = v[k-1] + k*(v[k] + v[k+1])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(5) }

Formula

Conjecture: A(n,0) = A006351(n+1).