A379458 Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + 2*(k+1)!*Sum_{j=0..k} A(n-1,j)/j! with A(0,k) = 1, n >= 0, k >= 0.

1, 1, 3, 1, 9, 15, 1, 31, 79, 109, 1, 129, 459, 835, 1053, 1, 651, 3003, 6885, 10661, 12767, 1, 3913, 22183, 61735, 114373, 161229, 186763, 1, 27399, 183975, 603565, 1307997, 2134803, 2830787, 3204313, 1, 219201, 1698819, 6424059, 15981869, 29753069, 44649839, 56720039, 63128665

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  |     3      9      31      129       651       3913 ...
2  |    15     79     459     3003     22183     183975 ...
3  |   109    835    6885    61735    603565    6424059 ...
4  |  1053  10661  114373  1307997  15981869  208612693 ...
5  | 12767 161229 2134803 29753069 437287383 6780218397 ...
  ...
		

Crossrefs

Cf. A217061.

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

Formula

Conjecture: A(n,0) = A217061(n+1).