A369595 Array read by downward antidiagonals: A(n,k) = A(n-1,k+2) + Sum_{j=0..k} binomial(k,j)*A(n-1,j) with A(0,k) = 1, n >= 0, k >= 0.

1, 1, 2, 1, 3, 7, 1, 5, 14, 37, 1, 9, 30, 89, 264, 1, 17, 68, 227, 737, 2433, 1, 33, 162, 611, 2169, 7696, 27913, 1, 65, 404, 1727, 6695, 25480, 98093, 386906, 1, 129, 1050, 5099, 21573, 87964, 358993, 1490687, 6346119, 1, 257, 2828, 15647, 72287, 315688, 1364681, 5959213, 26542518, 121159373

Offset

0,3

Links

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

Formula

Conjecture: A(n,0) = A135920(n+1). - Mikhail Kurkov, Oct 27 2024

Example

Array begins:
=============================================================
n\k|     0     1      2       3       4        5        6 ...
---+---------------------------------------------------------
0  |     1     1      1       1       1        1        1 ...
1  |     2     3      5       9      17       33       65 ...
2  |     7    14     30      68     162      404     1050 ...
3  |    37    89    227     611    1727     5099    15647 ...
4  |   264   737   2169    6695   21573    72287   251109 ...
5  |  2433  7696  25480   87964  315688  1174756  4522480 ...
6  | 27913 98093 358993 1364681 5376121 21901073 92076673 ...
  ...

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+2] + sum(j=1, k, binomial(k-1, j-1)*v[j])); r[1+i] = v[1..n+1]); Mat(r)}
{ A(6) }

Crossrefs

Cf. A135920.

Sequence in context: A073901 A116381 A176120 * A220621 A360587 A058170

Adjacent sequences: A369592 A369593 A369594 * A369596 A369597 A369598

Keyword

nonn,tabl

Author

Mikhail Kurkov, Jan 27 2024

Status

approved