A392095 Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + Sum_{j=0..k} A(n-1,j)*A(k-j,0) with A(0,k) = 1.

1, 1, 2, 1, 4, 6, 1, 10, 18, 24, 1, 34, 64, 94, 118, 1, 152, 278, 414, 556, 674, 1, 826, 1438, 2096, 2842, 3634, 4308, 1, 5134, 8528, 12046, 16110, 20772, 25754, 30062, 1, 35196, 56202, 76978, 100788, 128750, 160834, 195204, 225266, 1, 260462, 402638, 536728, 687578, 864906, 1073180, 1311370, 1566698, 1791964

Offset

0,3

Links

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

Formula

Conjecture: A(n,0) = A088713(n+1).

Example

Array begins:
=============================================================
n\k|    0     1      2       3       4        5         6 ...
---+---------------------------------------------------------
0  |    1     1      1       1       1        1         1 ...
1  |    2     4     10      34     152      826      5134 ...
2  |    6    18     64     278    1438     8528     56202 ...
3  |   24    94    414    2096   12046    76978    536728 ...
4  |  118   556   2842   16110  100788   687578   5052062 ...
5  |  674  3634  20772  128750  864906  6251224  48200006 ...
6  | 4308 25754 160834 1073180 7665010 58335158 470209888 ...
  ...

Prog

(PARI) antidiagonals(n) = {my(v = vector(n+1, i, vector(n-i+2, j, i==1)));
for(i=1, n, forstep(j=i-1, 0, -1, v[i-j+1][j+1] = v[i-j][j+2] + sum(k=0, j, v[i-j][k+1]*v[j-k+1][1])));
v = vector(n+1, i, vector(i, j, v[j][i-j+1]))}

Crossrefs

Cf. A088713.

Sequence in context: A079474 A091543 A330858 * A059575 A338805 A120769

Adjacent sequences: A392092 A392093 A392094 * A392096 A392097 A392098

Keyword

nonn,tabl

Author

Mikhail Kurkov, Dec 30 2025

Status

approved