A369292 Array read by downward antidiagonals: A(n,k) = -A(n-1,k) + (k+1)*A(n-1,k+1) + A(n-1,k+2) with A(0,k) = 1, n >= 0, k >= 0.

1, 1, 1, 1, 2, 4, 1, 3, 8, 18, 1, 4, 14, 42, 108, 1, 5, 22, 84, 276, 780, 1, 6, 32, 150, 612, 2160, 6600, 1, 7, 44, 246, 1212, 5220, 19560, 63840, 1, 8, 58, 378, 2196, 11280, 50880, 200760, 693840, 1, 9, 74, 552, 3708, 22260, 118560, 556920, 2299920, 8361360

Offset

0,5

Links

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

Example

Array begins:
=====================================================
n\k|    0     1     2      3      4      5      6 ...
---+-------------------------------------------------
0  |    1     1     1      1      1      1      1 ...
1  |    1     2     3      4      5      6      7 ...
2  |    4     8    14     22     32     44     58 ...
3  |   18    42    84    150    246    378    552 ...
4  |  108   276   612   1212   2196   3708   5916 ...
5  |  780  2160  5220  11280  22260  40800  70380 ...
6  | 6600 19560 50880 118560 252120 496920 919200 ...
  ...

Prog

(PARI)
A(m, n=m)={my(r=vectorv(m+1), v=vector(n+2*m+1, k, 1)); r[1] = v[1..n+1];
for(i=1, m, v=vector(#v-2, k, -v[k] + k*v[k+1] + v[k+2]); r[1+i] = v[1..n+1]); Mat(r)}
{ A(6) } \\ Andrew Howroyd, Jan 24 2024

Crossrefs

Column k=0 is A144085.

Rows n=0..2 are A000012, A000027(n+1), A014206(n+1).

Sequence in context: A366062 A208526 A275895 * A158613 A360859 A209573

Adjacent sequences: A369289 A369290 A369291 * A369293 A369294 A369295

Keyword

nonn,tabl,changed

Author

Mikhail Kurkov, Jan 24 2024

Status

approved