A383410 Array read by downward antidiagonals: A(n,k) = Sum_{i=0..n-1} Sum_{j=0..k+1} binomial(n-1,i)*binomial(k+1,j)*A(i,j) with A(0,k) = 1, n >= 0, k >= 0.

1, 1, 2, 1, 4, 8, 1, 8, 22, 44, 1, 16, 62, 154, 308, 1, 32, 178, 554, 1306, 2612, 1, 64, 518, 2038, 5690, 12994, 25988, 1, 128, 1522, 7634, 25366, 66338, 148282, 296564, 1, 256, 4502, 29014, 115298, 346366, 867002, 1908274, 3816548, 1, 512, 13378, 111554, 532726, 1844042, 5179798, 12564434, 27333706, 54667412

Offset: 0

Author

Mikhail Kurkov, Apr 26 2025

Keywords

• nonn
• tabl

Examples

			Array begins:
==================================================================
n\k|     0      1      2       3        4         5          6 ...
---+--------------------------------------------------------------
0  |     1      1      1       1        1         1          1 ...
1  |     2      4      8      16       32        64        128 ...
2  |     8     22     62     178      518      1522       4502 ...
3  |    44    154    554    2038     7634     29014     111554 ...
4  |   308   1306   5690   25366   115298    532726    2495570 ...
5  |  2612  12994  66338  346366  1844042   9985054   54865658 ...
6  | 25988 148282 867002 5179798 31540898 195320182 1227693842 ...
  ...
		

Crossrefs

Cf. A005649.

Programs

PARI

A(m, n=m)={my(r=vectorv(m+1), v=vector(m+1, j, vector(n+m-j+2, k, (j==1)))); r[1] = v[1][1..n+1];
for(i=1, m, v[i+1] = vector(#v[i+1], k, sum(j=1, i, sum(q=1, k+1, binomial(i-1,j-1)*binomial(k,q-1)*v[j][q]))); r[1+i] = v[i+1][1..n+1]); Mat(r)}
{ A(6) }

Formula

Conjecture: A(n,0) = A005649(n).